Advertisements
Advertisements
प्रश्न
State the following are not the probability distributions of a random variable. Give reasons for your answer.
| X | 0 | 1 | 2 | 3 | 4 |
| P(X) | 0.1 | 0.5 | 0.2 | -0.1 | 0.3 |
उत्तर
It is known that the sum of all the probabilities in a probability distribution is one.
It can be seen that for X = 3, P (X) = −0.1
It is known that probability of any observation is not negative. Therefore, the given table is not a probability distribution of random variables.
APPEARS IN
संबंधित प्रश्न
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.
| 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 |
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.
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation 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: c
Two cards are drawn successively without replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of aces.
A fair die is tossed twice. If the number appearing on the top is less than 3, it is a success. Find the probability distribution of number of successes.
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.
Find the mean and standard deviation of each of the following probability distribution :
| xi : | -5 | -4 | 1 | 2 |
| pi : | \[\frac{1}{4}\] | \[\frac{1}{8}\] | \[\frac{1}{2}\] | \[\frac{1}{8}\] |
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 cards are drawn simultaneously from a pack of 52 cards. Compute the mean and standard deviation of the number of kings.
A fair coin is tossed four times. Let X denote the longest string of heads occurring. Find the probability distribution, mean and variance of X.
If X denotes the number on the upper face of a cubical die when it is thrown, find the mean of X.
If a random variable X has the following probability distribution:
| X : | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| P (X) : | a | 3a | 5a | 7a | 9a | 11a | 13a | 15a | 17a |
then the value of a is
Mark the correct alternative in the following question:
The probability distribution of a discrete random variable X is given below:
| X: | 2 | 3 | 4 | 5 |
| P(X): |
\[\frac{5}{k}\]
|
\[\frac{7}{k}\]
|
\[\frac{9}{k}\]
|
\[\frac{11}{k}\] |
The value of k is .
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.
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)
Write the negation of the following statements :
(a) Chetan has black hair and blue eyes.
(b) ∃ x ∈ R such that x2 + 3 > 0.
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
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).
An urn contains 5 red and 2 black balls. Two balls are drawn at random. X denotes number of black balls drawn. What are possible values of X?
Find expected value and variance of X, where X is number obtained on uppermost face when a fair die is thrown.
Determine whether each of the following is a probability distribution. Give reasons for your answer.
| z | 3 | 2 | 1 | 0 | -1 |
| P(z) | 0.3 | 0.2 | 0.4. | 0.05 | 0.05 |
Determine whether each of the following is a probability distribution. Give reasons for your answer.
| y | –1 | 0 | 1 |
| P(y) | 0.6 | 0.1 | 0.2 |
A pair of dice is thrown 3 times. If getting a doublet is considered a success, find the probability of two successes
There are 10% defective items in a large bulk of items. What is the probability that a sample of 4 items will include not more than one defective item?
Defects on plywood sheet occur at random with the average of one defect per 50 Sq.ft. Find the probability that such a sheet has no defect
Defects on plywood sheet occur at random with the average of one defect per 50 sq.ft. Find the probability that such a sheet has:
- no defect
- at least one defect
Use e−1 = 0.3678
Let the p.m.f. of a random variable X be P(x) = `(3 - x)/10`, for x = −1, 0, 1, 2 = 0, otherwise Then E(x) is ______
Find the probability distribution of the number of doublets in three throws of a pair of dice
Consider the probability distribution of a random variable X:
| X | 0 | 1 | 2 | 3 | 4 |
| P(X) | 0.1 | 0.25 | 0.3 | 0.2 | 0.15 |
Calculate `"V"("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 Standard deviation 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 P(X ≥ 4)
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 ______.
Two balls are drawn at random one by one with replacement from an urn containing equal number of red balls and green balls. Find the probability distribution of number of red balls. Also, find the mean of the random variable.
