Applied Mathematics

Probability Distribution

Medium

applied

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If $P(X=1) = 0.4$ , $P(X=4) = P(X=2)$ and $P(X=3) = 2P(X=2)$ , then $P(X=0)$ is :

0.2

0.1

0.4

0.3

✅ Correct Option: 1

Let $P(X=2) = a$ . Then $P(X=4) = a$ , $P(X=3) = 2a$ .

Mean: $0.4 + 2a + 6a + 4a = 1.6 \Rightarrow 12a = 1.2 \Rightarrow a = 0.1$ .

Sum $= 1$ : $P(0) + 0.4 + 0.1 + 0.2 + 0.1 = 1 \Rightarrow P(0) = 0.2$ .

2023: 22 May Shift 3

If a random variable X follows binomial distribution with mean 5 and variance $\frac{5}{2}$ , then $P(X \leq 9)$ is :

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: 14 May Shift 2

In a random experiment, a collection of trials is called Bernoulli trials if

A. The number of trials is infinite.

B. The trials are independent of each other.

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

D. The probability of success will vary in each trial.

Choose the correct answer from the options given below:

2026: 19 May Shift 2

A car hire firm has two cars, which is hire out day by day. The number of demands for cars on each day is distributed as a Poisson distribution with mean 1.5. Then which of the following is/are TRUE? (use $e^{-1.5} = 0.2231$ )

A. The probability of days when no car is required is 0.2231

B. The probability of days when some demand is refused is 0.1913

C. The probability of days when no car is required is 0.1913

D. The probability of days when some demand is refused is 0.2231

Choose the correct answer from the options given below:

2026: 19 May Shift 2

If $X$ is a discrete random variable which assumes values $x_1, x_2, x_3, ..., x_n$ with the respective probabilities $p_1, p_2, ....., p_n$ , then

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$\displaystyle\sum_{i=1}^{n} p_i =$	I.	$E(X^2)$
B.	$\displaystyle\sum_{i=1}^{n} p_i x_i =$	II.	$Var(X)$
C.	$\displaystyle\sum_{i=1}^{n} p_i x_i^2 =$	III.	$1$
D.	$E(X^2) - \{E(X)\}^2 =$	IV.	$E(X)$

Choose the correct answer from the options given below:

2026: 30 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Mean of a normal variate X is 12 and standard deviation is 4, then the Z-score of data point 20 is	(I) 1
(B) If X is Poisson variate such that P(X=1) = 2P(X=2), then the mean of X is	(II) 8
(C) In a binomial distribution, if mean is 5 and variance is 4, then the number of trials is	(III) 2
(D) In a binomial distribution, if n = 20 and q = 0.6, then its mean is	(IV) 25

Choose the correct answer from the options given below:

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If P(X=1)=0.4P(X=1) = 0.4P(X=1)=0.4, P(X=4)=P(X=2)P(X=4) = P(X=2)P(X=4)=P(X=2) and P(X=3)=2P(X=2)P(X=3) = 2P(X=2)P(X=3)=2P(X=2), then P(X=0)P(X=0)P(X=0) is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If $P(X=1) = 0.4$ , $P(X=4) = P(X=2)$ and $P(X=3) = 2P(X=2)$ , then $P(X=0)$ is :