A random variable X has the following probability distribution

then value of E(X) is :

3.66

The correct answer is Option (3) → 3.66

The probabilities are given at,

$P(X)=0,k,2k,2k,3k,k^2,2k^2,7k^2+k$

The sum of all probabilities must be equal to 1.

$⇒0+k+2k+2k+3k+k^2+2k^2+7k^2+k$

$⇒10k^2+9k=1$

$⇒10k^2+9k-1=0$

$⇒10k^2+10k-k-1=0$

$⇒10k(k+1)-(k+1)=0$

$⇒(k+1)(10k-1)=0$

$⇒k=\frac{1}{10}$  [always positive]

$=0.1$

$∴E(X)=∑X.P(X)$

$=(0.0)+(1×0.1)+(2×0.2)+(4×0.3)+(5×0.01)+(6×2×0.01)+[7(7×0.01+0.1)]$

$=3.66$