Applied Mathematics

Probability Distribution

Medium

applied

If the probability distribution of a random variable X is given as

$x_i$ 0 1 2 3
$p_i$ $2k^2$ $k^2$ $3k^2$ $k$

Then the mean of X is

$x_i$	0	1	2	3
$p_i$	$2k^2$	$k^2$	$3k^2$	$k$

$\frac{8}{9}$

$\frac{4}{9}$

$\frac{14}{9}$

$\frac{16}{9}$

✅ Correct Option: 4

Sum of probabilities $= 1$ : $6k^2 + k = 1$ , i.e. $6k^2 + k - 1 = 0$ . Solving: $k = \frac{-1 + 5}{12} = \frac{1}{3}$ (positive root).

Mean $= \sum x_i p_i = 0 + k^2 + 6k^2 + 3k = 7k^2 + 3k = \frac{7}{9} + 1 = \frac{16}{9}$ .

2023: 22 May Shift 3

If the probability distribution of X is :

X	2	3	4	5	6
P(X)	1/15	2/15	3/15	4/15	5/15

Then variance is equal to :

2026: 29 May Shift 2

The probability distribution of a discrete random variable is given below :

X	1	2	3	4	5
P(X)	1/5	m	2/5	2m	3m

Which of the following are correct?

A. $P(2)=\frac{1}{15}$

B. $P(4)=\frac{2}{15}$

C. $P(X<2)=\frac{1}{5}$

D. $P(X\geq4)=\frac{1}{5}$

Choose the correct answer from the options given below:

2022: 25 May Shift 1

Match List I with List II

LIST I	LIST II
A. The variance of a Poisson distribution with mean $\lambda$ is	I. $\sqrt{\lambda}$
B. The standard deviation of a Poisson distribution with mean $\lambda$ is	II. 4
C. In a Poisson distribution, if mean is 4, then the standard deviation is	III. $\lambda$
D. In a Poisson distribution, if mean is 4, then the variance is	IV. 2

Choose the correct answer from the options given below:

2023: 11 Aug Shift 1

In a binomial distribution the probability of getting success is $\frac{1}{4}$ And standard deviation is 3 then its mean is ?

2026: 29 May Shift 2

If 0.1% of the bolts manufactured by a machine are found to be defective. Find the probability that, in a sample of 2000 bolts chosen at random, exactly 3 will be defective using the Poisson distribution. [Given $e^{-2} =0.1353$ ]

2023: 11 Aug Shift 1

10 works hard drawn successively with replacement from a lot containing 10% defective bulb. The probability that there is at least one defective bulb is :

If the probability distribution of a random variable X is given as xix_ixi​0123pip_ipi​2k22k^22k2k2k^2k23k23k^23k2kkk Then the mean of X is

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CUET Mathematics Past Year Questions (Topic-Wise)

If the probability distribution of a random variable X is given as

$x_i$ 0 1 2 3
$p_i$ $2k^2$ $k^2$ $3k^2$ $k$

Then the mean of X is