Advertisements
Advertisements
प्रश्न
For the random variable X, if V(X) = 4, E(X) = 3, then E(x2) is ______
पर्याय
9
13
12
7
उत्तर
13
संबंधित प्रश्न
A random variable X has the following probability distribution:
then E(X)=....................
Probability distribution of X is given by
| X = x | 1 | 2 | 3 | 4 |
| P(X = x) | 0.1 | 0.3 | 0.4 | 0.2 |
Find P(X ≥ 2) and obtain cumulative distribution function of X
Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is hostler?
State the following are not the probability distributions of a random variable. Give reasons for your answer.
| X | 0 | 1 | 2 |
| P (X) | 0.4 | 0.4 | 0.2 |
State the following are not the probability distributions of a random variable. Give reasons for your answer.
| Y | -1 | 0 | 1 |
| P(Y) | 0.6 | 0.1 | 0.2 |
An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represents the number of black balls. What are the possible values of X? Is X a random variable?
Find the probability distribution of number of tails in the simultaneous tosses of three coins.
Find the probability distribution of number of heads in four tosses of a coin.
From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.
The random variable X has probability distribution P(X) of the following form, where k is some number:
`P(X = x) {(k, if x = 0),(2k, if x = 1),(3k, if x = 2),(0, "otherwise"):}`
- Determine the value of 'k'.
- Find P(X < 2), P(X ≥ 2), P(X ≤ 2).
Assume that the chances of the patient having a heart attack are 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?
Two numbers are selected at random (without replacement) from the first five positive integers. Let X denote the larger of the two numbers obtained. Find the mean and variance of X
Let, X denote the number of colleges where you will apply after your results and P(X = x) denotes your probability of getting admission in x number of colleges. It is given that
where k is a positive constant. Find the value of k. Also find the probability that you will get admission in (i) exactly one college (ii) at most 2 colleges (iii) at least 2 colleges.
Five defective mangoes are accidently mixed with 15 good ones. Four mangoes are drawn at random from this lot. Find the probability distribution of the number of defective mangoes.
Five defective bolts are accidently mixed with twenty good ones. If four bolts are drawn at random from this lot, find the probability distribution of the number of defective bolts.
Two cards are drawn successively with replacement from well shuffled pack of 52 cards. Find the probability distribution of the number of aces.
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of kings.
Find the probability distribution of Y in two throws of two dice, where Y represents the number of times a total of 9 appears.
An urn contains 4 red and 3 blue balls. Find the probability distribution of the number of blue balls in a random draw of 3 balls with replacement.
Two cards are drawn simultaneously from a well-shuffled deck of 52 cards. Find the probability distribution of the number of successes, when getting a spade is considered a success.
From a lot of 10 bulbs, which includes 3 defectives, a sample of 2 bulbs is drawn at random. Find the probability distribution of the number of defective bulbs.
Four balls are to be drawn without replacement from a box containing 8 red and 4 white balls. If X denotes the number of red balls drawn, then find the probability distribution of X.
The probability distribution of a random variable X is given below:
| x | 0 | 1 | 2 | 3 |
| P(X) | k |
\[\frac{k}{2}\]
|
\[\frac{k}{4}\]
|
\[\frac{k}{8}\]
|
Find P(X ≤ 2) + P(X > 2) .
Find the mean and standard deviation of each of the following probability distribution:
| xi : | 1 | 3 | 4 | 5 |
| pi: | 0.4 | 0.1 | 0.2 | 0.3 |
Find the mean and standard deviation of each of the following probability distribution :
| xi : | -5 | -4 | 1 | 2 |
| pi : | \[\frac{1}{4}\] | \[\frac{1}{8}\] | \[\frac{1}{2}\] | \[\frac{1}{8}\] |
Find the mean and standard deviation of each of the following probability distribution :
| xi : | 0 | 1 | 2 | 3 | 4 | 5 |
| pi : |
\[\frac{1}{6}\]
|
\[\frac{5}{18}\]
|
\[\frac{2}{9}\]
|
\[\frac{1}{6}\]
|
\[\frac{1}{9}\]
|
\[\frac{1}{18}\]
|
A discrete random variable X has the probability distribution given below:
| X: | 0.5 | 1 | 1.5 | 2 |
| P(X): | k | k2 | 2k2 | k |
Find the value of k.
Find the mean variance and standard deviation of the following probability distribution
| xi : | a | b |
| pi : | p | q |
Two bad eggs are accidently mixed up with ten good ones. Three eggs are drawn at random with replacement from this lot. Compute the mean for the number of bad eggs drawn.
Two cards are selected at random from a box which contains five cards numbered 1, 1, 2, 2, and 3. Let X denote the sum and Y the maximum of the two numbers drawn. Find the probability distribution, mean and variance of X and Y.
In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.
If the probability distribution of a random variable X is given by Write the value of k.
| X = xi : | 1 | 2 | 3 | 4 |
| P (X = xi) : | 2k | 4k | 3k | k |
Find the mean of the following probability distribution:
| X= xi: | 1 | 2 | 3 |
| P(X= xi) : |
\[\frac{1}{4}\]
|
\[\frac{1}{8}\]
|
\[\frac{5}{8}\]
|
If the probability distribution of a random variable X is as given below:
Write the value of P (X ≤ 2).
| X = xi : | 1 | 2 | 3 | 4 |
| P (X = xi) : | c | 2c | 4c | 4c |
A random variable has the following probability distribution:
| X = xi : | 1 | 2 | 3 | 4 |
| P (X = xi) : | k | 2k | 3k | 4k |
Write the value of P (X ≥ 3).
A random variable X takes the values 0, 1, 2, 3 and its mean is 1.3. If P (X = 3) = 2 P (X = 1) and P (X = 2) = 0.3, then P (X = 0) is
A random variable has the following probability distribution:
| X = xi : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| P (X = xi) : | 0 | 2 p | 2 p | 3 p | p2 | 2 p2 | 7 p2 | 2 p |
The value of p is
If X is a random-variable with probability distribution as given below:
| X = xi : | 0 | 1 | 2 | 3 |
| P (X = xi) : | k | 3 k | 3 k | k |
The value of k and its variance are
Mark the correct alternative in the following question:
For the following probability distribution:
| X: | −4 | −3 | −2 | −1 | 0 |
| P(X): | 0.1 | 0.2 | 0.3 | 0.2 | 0.2 |
The value of E(X) is
Mark the correct alternative in the following question:
Let X be a discrete random variable. Then the variance of X is
A die is tossed twice. A 'success' is getting an even number on a toss. Find the variance of number of successes.
Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spades. Hence, find the mean of the distribtution.
Let X be a random variable which assumes values x1 , x2, x3 , x4 such that 2P (X = x1) = 3P (X = x2) = P (X = x3) = 5P (X = x4). Find the probability distribution of X.
Calculate `"e"_0^circ ,"e"_1^circ , "e"_2^circ` from the following:
| Age x | 0 | 1 | 2 |
| lx | 1000 | 880 | 876 |
| Tx | - | - | 3323 |
The following data gives the marks of 20 students in mathematics (X) and statistics (Y) each out of 10, expressed as (x, y). construct ungrouped frequency distribution considering single number as a class :
(2, 7) (3, 8) (4, 9) (2, 8) (2, 8) (5, 6) (5 , 7) (4, 9) (3, 8) (4, 8) (2, 9) (3, 8) (4, 8) (5, 6) (4, 7) (4, 7) (4, 6 ) (5, 6) (5, 7 ) (4, 6 )
Find mean and standard deviation of the continuous random variable X whose p.d.f. is given by f(x) = 6x(1 - x);= (0); 0 < x < 1(otherwise)
If p : It is a day time , q : It is warm
Give the verbal statements for the following symbolic statements :
(a) p ∧ ∼ q (b) p v q (c) p ↔ q
If X ∼ N (4,25), then find P(x ≤ 4)
The defects on a plywood sheet occur at random with an average of the defect per 50 sq. ft. What Is the probability that such sheet will have-
(a) No defects
(b) At least one defect
[Use e-1 = 0.3678]
The probability that a bomb dropped from an aeroplane will strike a target is `1/5`, If four bombs are dropped, find the probability that :
(a) exactly two will strike the target,
(b) at least one will strike the target.
Solve the following :
Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.
20 white rats are available for an experiment. Twelve rats are male. Scientist randomly selects 5 rats number of female rats selected on a specific day
Solve the following:
Identify the random variable as either discrete or continuous in each of the following. Write down the range of it.
A highway safety group is interested in studying the speed (km/hrs) of a car at a check point.
The p.d.f. of a continuous r.v. X is given by
f (x) = `1/ (2a)` , for 0 < x < 2a and = 0, otherwise. Show that `P [X < a/ 2] = P [X >( 3a)/ 2]` .
The p.d.f. of r.v. of X is given by
f (x) = `k /sqrtx` , for 0 < x < 4 and = 0, otherwise. Determine k .
Determine c.d.f. of X and hence P (X ≤ 2) and P(X ≤ 1).
Determine whether each of the following is a probability distribution. Give reasons for your answer.
| x | 0 | 1 | 2 | 3 | 4 |
| P(x) | 0.1 | 0.5 | 0.2 | –0.1 | 0.3 |
Determine whether each of the following is a probability distribution. Give reasons for your answer.
| x | 0 | 1 | 2 |
| P(x) | 0.1 | 0.6 | 0.3 |
Find the probability distribution of the number of successes in two tosses of a die if success is defined as getting a number greater than 4.
A coin is biased so that the head is 3 times as likely to occur as tail. Find the probability distribution of number of tails in two tosses.
A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. If X denotes the age of a randomly selected student, find the probability distribution of X. Find the mean and variance of X.
A die is thrown 4 times. If ‘getting an odd number’ is a success, find the probability of 2 successes
A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of two successes
The probability that a bulb produced by a factory will fuse after 200 days of use is 0.2. Let X denote the number of bulbs (out of 5) that fuse after 200 days of use. Find the probability of X ≤ 1
The probability that a bulb produced by a factory will fuse after 200 days of use is 0.2. Let X denote the number of bulbs (out of 5) that fuse after 200 days of use. Find the probability of (i) X = 0, (ii) X ≤ 1, (iii) X > 1, (iv) X ≥ 1.
Solve the following problem :
Following is the probability distribution of a r.v.X.
| x | – 3 | – 2 | –1 | 0 | 1 | 2 | 3 |
| P(X = x) | 0.05 | 0.1 | 0.15 | 0.20 | 0.25 | 0.15 | 0.1 |
Find the probability that X is non-negative
Solve the following problem :
Find the probability of the number of successes in two tosses of a die, where success is defined as number greater than 4.
Solve the following problem :
If a fair coin is tossed 4 times, find the probability that it shows 3 heads
Solve the following problem :
The probability that a lamp in the classroom will burn is 0.3. 3 lamps are fitted in the classroom. The classroom is unusable if the number of lamps burning in it is less than 2. Find the probability that the classroom cannot be used on a random occasion.
Solve the following problem :
A large chain retailer purchases an electric device from the manufacturer. The manufacturer indicates that the defective rate of the device is 10%. The inspector of the retailer randomly selects 4 items from a shipment. Find the probability that the inspector finds at most one defective item in the 4 selected items.
Solve the following problem :
A computer installation has 3 terminals. The probability that any one terminal requires attention during a week is 0.1, independent of other terminals. Find the probabilities that 0
Solve the following problem :
A computer installation has 3 terminals. The probability that any one terminal requires attention during a week is 0.1, independent of other terminals. Find the probabilities that 1 terminal requires attention during a week.
Solve the following problem :
In a large school, 80% of the students like mathematics. A visitor asks each of 4 students, selected at random, whether they like mathematics.
Find the probability that the visitor obtains the answer yes from at least 3 students.
Find the probability distribution of the number of doublets in three throws of a pair of dice
Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as six appears on at least one die
A discrete random variable X has the probability distribution given as below:
| X | 0.5 | 1 | 1.5 | 2 |
| P(X) | k | k2 | 2k2 | k |
Determine the mean of the distribution.
The probability distribution of a random variable X is given below:
| X | 0 | 1 | 2 | 3 |
| P(X) | k | `"k"/2` | `"k"/4` | `"k"/8` |
Determine the value of k.
The probability distribution of a random variable X is given below:
| X | 0 | 1 | 2 | 3 |
| P(X) | k | `"k"/2` | `"k"/4` | `"k"/8` |
Find P(X ≤ 2) + P (X > 2)
Two probability distributions of the discrete random variable X and Y are given below.
| X | 0 | 1 | 2 | 3 |
| P(X) | `1/5` | `2/5` | `1/5` | `1/5` |
| Y | 0 | 1 | 2 | 3 |
| P(Y) | `1/5` | `3/10` | `2/10` | `1/10` |
Prove that E(Y2) = 2E(X).
Let X be a discrete random variable whose probability distribution is defined as follows:
P(X = x) = `{{:("k"(x + 1), "for" x = 1"," 2"," 3"," 4),(2"k"x, "for" x = 5"," 6"," 7),(0, "Otherwise"):}`
where k is a constant. Calculate Standard deviation of X.
The probability distribution of a discrete random variable X is given as under:
| X | 1 | 2 | 4 | 2A | 3A | 5A |
| P(X) | `1/2` | `1/5` | `3/25` | `1/10` | `1/25` | `1/25` |
Calculate: Variance of X
The probability distribution of a random variable x is given as under:
P(X = x) = `{{:("k"x^2, "for" x = 1"," 2"," 3),(2"k"x, "for" x = 4"," 5"," 6),(0, "otherwise"):}`
where k is a constant. Calculate E(X)
For the following probability distribution:
| X | 1 | 2 | 3 | 4 |
| P(X) | `1/10` | `3/10` | `3/10` | `2/5` |
E(X2) is equal to ______.
A bag contains 1 red and 3 white balls. Find the probability distribution of the number of red balls if 2 balls are drawn at random from the bag one-by-one without replacement.
A person throws two fair dice. He wins ₹ 15 for throwing a doublet (same numbers on the two dice), wins ₹ 12 when the throw results in the sum of 9, and loses ₹ 6 for any other outcome on the throw. Then the expected gain/loss (in ₹) of the person is ______.
A large chain retailer purchases an electric device from the manufacturer. The manufacturer indicates that the defective rate of the device is 10%. The inspector of the retailer randomly selects 4 items from a shipment. Complete the following activity to find the probability that the inspector finds at most one defective item in the 4 selected items.
Solution:
Here, n = 4
p = probability of defective device = 10% = `10/100 = square`
∴ q = 1 - p = 1 - 0.1 = `square`
X ∼ B(4, 0.1)
`P(X=x)=""^n"C"_x p^x q^(n-x)= ""^4"C"_x (0.1)^x (0.9)^(4 - x)`
P[At most one defective device] = P[X ≤ 1]
= P[X=0] + P[X=1]
= `square+square`
∴ P[X ≤ 1] = `square`
