Question

A random variable X and its probability distribution is given below. The value of P(X<5) is _______. (rounded off to one decimal place)

X	0	1	2	3	4	5
P(X)	0	K	2K	3K	4K	5K

Answer 1

Correct Answer: 0.6

Given:
Random variable \(X\) and probabilities:  
\[ X: 0, 1, 2, 3, 4, 5 \] \[ P(X): 0, K, 2K, 3K, 4K, 5K \] 
Step 1 — Find K using total probability:
\[ \sum_{x=0}^{5} P(X) = 1 \] \[ 0 + K + 2K + 3K + 4K + 5K = 15K = 1 \] \[ K = \frac{1}{15} \approx 0.0667 \] 
Step 2 — Compute \(P(X < 5)\):
\[ P(X<5) = P(0) + P(1) + P(2) + P(3) + P(4) \] \[ P(X<5) = 0 + K + 2K + 3K + 4K = 10K \] \[ P(X<5) = 10 \cdot \frac{1}{15} = \frac{2}{3} \approx 0.667 \] Step 3 — Round to one decimal place:
\[ \boxed{0.6} \]