Advertisements
Advertisements
प्रश्न
A random variable X has the following probability distribution:
then E(X)=....................
विकल्प
0.8
0.9
0.7
1.1
उत्तर
(a) 0.8
X = x |
-2 |
-1 |
0 |
1 |
2 |
3 |
P(x) |
0.1 |
0.1 |
0.2 |
0.2 |
0.3 |
0.1 |
`E(X)=sumx_iP(x_i)`
=( -2) x 0.1 + ( -1) x 0.1+ 0 x 0.2 +1x 0.2+ 2 x 0.3 + 3 x 0.1
= - 0.2 - 0.1 + 0 + 0.2 + 0.6 + 0.3
=0.8
APPEARS IN
संबंधित प्रश्न
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 |
State the following are not the probability distributions of a random variable. Give reasons for your answer.
Z | 3 | 2 | 1 | 0 | -1 |
P(Z) | 0.3 | 0.2 | 0.4 | 0.1 | 0.05 |
A random variable X ~ N (0, 1). Find P(X > 0) and P(X < 0).
There are 4 cards numbered 1, 3, 5 and 7, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. Find the mean 'and variance of X.
There are 4 cards numbered 1 to 4, one number on one card. Two cards are drawn at random without replacement. Let X denote the sum of the numbers on the two drawn cards. 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.
The probability distribution function of a random variable X is given by
xi : | 0 | 1 | 2 |
pi : | 3c3 | 4c − 10c2 | 5c-1 |
where c > 0 Find: P (1 < X ≤ 2)
A random variable X takes the values 0, 1, 2 and 3 such that:
P (X = 0) = P (X > 0) = P (X < 0); P (X = −3) = P (X = −2) = P (X = −1); P (X = 1) = P (X = 2) = P (X = 3) . Obtain the probability distribution of X.
Two cards are drawn from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.
Four cards are drawn simultaneously from a well shuffled pack of 52 playing cards. Find the probability distribution of the number of aces.
Find the probability distribution of Y in two throws of two dice, where Y represents the number of times a total of 9 appears.
The probability distribution of a random variable X is given below:
x | 0 | 1 | 2 | 3 |
P(X) | k |
\[\frac{k}{2}\]
|
\[\frac{k}{4}\]
|
\[\frac{k}{8}\]
|
Determine the value of k .
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.
Find the mean and standard deviation of each of the following probability distribution :
xi: | 0 | 1 | 3 | 5 |
pi : | 0.2 | 0.5 | 0.2 | 0.1 |
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.
A fair die is tossed. Let X denote twice the number appearing. Find the probability distribution, mean and variance of X.
In roulette, Figure, the wheel has 13 numbers 0, 1, 2, ...., 12 marked on equally spaced slots. A player sets Rs 10 on a given number. He receives Rs 100 from the organiser of the game if the ball comes to rest in this slot; otherwise he gets nothing. If X denotes the player's net gain/loss, find E (X).
Three cards are drawn at random (without replacement) from a well shuffled pack of 52 cards. Find the probability distribution of number of red cards. Hence, find the mean of the distribution .
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.
Write the values of 'a' for which the following distribution of probabilities becomes a probability distribution:
X= xi: | -2 | -1 | 0 | 1 |
P(X= xi) : |
\[\frac{1 - a}{4}\]
|
\[\frac{1 + 2a}{4}\]
|
\[\frac{1 - 2a}{4}\]
|
\[\frac{1 + a}{4}\]
|
For what value of k the following distribution is a probability distribution?
X = xi : | 0 | 1 | 2 | 3 |
P (X = xi) : | 2k4 | 3k2 − 5k3 | 2k − 3k2 | 3k − 1 |
If X denotes the number on the upper face of a cubical die when it is thrown, find the mean of X.
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 pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of the number of successes and, hence, find its mean.
A die is tossed twice. A 'success' is getting an even number on a toss. Find the variance of number of successes.
An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also find mean and variance of the distribution.
Five bad oranges are accidently mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence find the mean and variance of the distribution.
Demand function x, for a certain commodity is given as x = 200 - 4p where p is the unit price. Find :
(a) elasticity of demand as function of p.
(b) elasticity of demand when p = 10 , interpret your result.
Compute the age specific death rate for the following data :
Age group (years) | Population (in thousands) | Number of deaths |
Below 5 | 15 | 360 |
5-30 | 20 | 400 |
Above 30 | 10 | 280 |
A random variable X has the following probability distribution :
X = x | -2 | -1 | 0 | 1 | 2 | 3 |
P(x) | 0.1 | k | 0.2 | 2k | 0.3 | k |
Find the value of k and calculate mean.
A fair coin is tossed 12 times. Find the probability of getting at least 2 heads .
Write the negation of the following statements :
(a) Chetan has black hair and blue eyes.
(b) ∃ x ∈ R such that x2 + 3 > 0.
The expenditure Ec of a person with income I is given by Ec = (0.000035) I2 + (0. 045) I. Find marginal propensity to consume (MPC) and average propensity to consume (APC) when I = 5000.
Alex spends 20% of his income on food items and 12% on conveyance. If for the month of June 2010, he spent ₹900 on conveyance, find his expenditure on food items during the same month.
The p.m.f. of a random variable X is
`"P"(x) = 1/5` , for x = I, 2, 3, 4, 5
= 0 , otherwise.
Find E(X).
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 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.
10 balls are marked with digits 0 to 9. If four balls are selected with replacement. What is the probability that none is marked 0?
In a multiple choice test with three possible answers for each of the five questions, what is the probability of a candidate getting four or more correct answers by random choice?
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 positive.
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:
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 odd.
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 :
Find the probability of the number of successes in two tosses of a die, where success is defined as six appears in at least one toss.
Solve the following problem :
If a fair coin is tossed 4 times, find the probability that it shows head in the first 2 tosses and tail in last 2 tosses.
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 :
It is observed that it rains on 10 days out of 30 days. Find the probability that it rains on exactly 3 days of a week.
Solve the following problem :
It is observed that it rains on 10 days out of 30 days. Find the probability that it rains on at most 2 days of a week.
For the random variable X, if V(X) = 4, E(X) = 3, then E(x2) is ______
Find the mean and variance of the number randomly selected from 1 to 15
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 P(X ≤ 2) and P(X > 2)
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 the value of k
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 E(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.
Find the mean number of defective items in a sample of two items drawn one-by-one without replacement from an urn containing 6 items, which include 2 defective items. Assume that the items are identical in shape and size.
Two numbers are selected from first six even natural numbers at random without replacement. If X denotes the greater of two numbers selected, find the probability distribution of X.
A box contains 30 fruits, out of which 10 are rotten. Two fruits are selected at random one by one without replacement from the box. Find the probability distribution of the number of unspoiled fruits. Also find the mean of the probability distribution.
Five numbers x1, x2, x3, x4, x5 are randomly selected from the numbers 1, 2, 3, ......., 18 and are arranged in the increasing order such that x1 < x2 < x3 < x4 < x5. What is the probability that x2 = 7 and x4 = 11?