Algebra

Probability

Easy

common

A random variable X has the following probability distribution:

X 2 3 4 5
P(X) 5/k 7/k 9/k 11/k

Then the value of $\frac{k}{4}$ is:

X	2	3	4	5
P(X)	5/k	7/k	9/k	11/k

✅ Correct Option: 1

For any probability distribution, all probabilities must add up to 1.

From the table:

$P(X = 2) = \frac{5}{k}$

$P(X = 3) = \frac{7}{k}$

$P(X = 4) = \frac{9}{k}$

$P(X = 5) = \frac{11}{k}$

All probabilities sum to 1:

$\frac{5}{k} + \frac{7}{k} + \frac{9}{k} + \frac{11}{k} = 1$

Since all fractions have the same denominator:

$\frac{5 + 7 + 9 + 11}{k} = 1$

$\frac{32}{k} = 1$

$32 = k$

Therefore $k = 32$

$\frac{k}{4} = \frac{32}{4}$

$\frac{k}{4} = 8$

Therefore, the value of $\frac{k}{4}$ is $8$ .

2025: 30 May Shift 2

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X	-2	-1	0	1	2
P(X)	2/11	1/11	4/11	3/11	1/11

Then the value of E(X) is

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X	0	1	2	3
P(X)	0.1	0.2	0.3	0.4

The variance of the X will be:

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X	0	1	2
P(X)	$1 - 7a^2$	$\frac{1}{2}a + \frac{1}{4}$	$a^2$

If $a > 0$ , then $P(0 < x \leq 2)$ is equal to

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A random variable X has the following probability distribution: X2345P(X)5/k7/k9/k11/k Then the value of k4\frac{k}{4}4k​ is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

A random variable X has the following probability distribution:

X 2 3 4 5
P(X) 5/k 7/k 9/k 11/k

Then the value of $\frac{k}{4}$ is: