Applied Mathematics

Probability Distribution

Easy

applied

A random variable X follows Poisson distribution. The variance of X is 2. The value of $P(X=3)$ is

$\dfrac{3}{4e^2}$

$\dfrac{4}{3e^2}$

$\dfrac{3e^2}{4}$

$\dfrac{4e^2}{3}$

✅ Correct Option: 2

For a Poisson variable the variance equals the mean, so $\lambda = 2$ .

$P(X=3) = \dfrac{e^{-2}2^3}{3!} = \dfrac{8}{6e^2} = \dfrac{4}{3e^2}$ .

2023: 11 Aug Shift 1

The variance of the number of heads in two tosses of a coin is :

2026: 29 May Shift 2

In a binomial distribution, the sum of its mean and variance is 1.8. If the event was conducted 5 times, then the probability of 3 successes is

2026: 25 May Shift 1

If X is a random variable which can take values 0,1,2,3 such that $E(X^2) = 2E(X)$ .

If $P(X=0) = P(X=1) = m\ \&\ P(X=2) = 2m$ , then which of the following are TRUE?

A. $P(X=1) = \dfrac{1}{13}$

B. $P(X=3) = \dfrac{1}{13}$

C. $E(X) = \dfrac{18}{13}$

D. $P(X=2) = \dfrac{6}{13}$

Choose the correct answer from the options given below:

2022: 25 May Shift 1

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

X	0	1	2	3	4
P(X)	0.5	2k	3k	3k	2k

Then the value of $k$ is:

2026: 25 May Shift 1

If a random variable X follows poisson's distribution such that $P(X=2) = 9P(X=4) + 90P(X=6)$ , then the mean of X is

2026: 26 May Shift 2

In a random experiment, a collection of trials is called Bernoulli trials then which of the following statements are TRUE?

A. The number of trials is infinite.

B. Each trial has exactly two outcomes defined as success and failure.

C. The trials are dependent by nature.

D. The probability of success remains the same in each trial.

Choose the correct answer from the options given below:

A random variable X follows Poisson distribution. The variance of X is 2. The value of P(X=3)P(X=3)P(X=3) is