The probability distribution of a random

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

The probability distribution of a random variable x is given below

P(X – x)

$\frac{k}{2}$

$\frac{k}{4}$

$\frac{k}{8}$

Then P(X ≤ 2) is

Options:

$\frac{12}{15}$

$\frac{14}{15}$

$\frac{8}{15}$

$\frac{2}{15}$

Correct Answer:

$\frac{14}{15}$

Explanation:

Find value of K by P(x) = 1

$∴ \frac{k}{1}+\frac{k}{2}+\frac{k}{4}+\frac{k}{8}=1⇒k=\frac{8}{15}$

P(x ≤ 2) = 1 - P(x = 3) = $1-\frac{k}{8}=1-\frac{8}{15×8}$

$1-\frac{1}{15}=\frac{14}{15}$