If the p.d.f of a continuous random variable. X is \(f(x)=\left\{\begin{array}{l} \frac{x}{2}, 0 then E(3X²-2X) = _________

The random variable. X has variance 4 and E(X²) = 8. Then the mean of X is __________

If \(f(x)=\left\{\begin{array}{cc} \frac{A}{x}, & 1<x<e^{3} \\ 0, & \text { otherwise } \end{array}\right.\) is a p.d.f. of a continuous random variable. X then P(X≥e)

A probability distribution function is defined by \(F(x)\begin{cases} 0,\ x<0 \\ 1-{ e }^{ -x },\ x\ge 0 \end{cases}\) The probability density function is __________

If f(x) = cx², 0

If E(X)  = \(\frac{1}{2}, E(X^2)=\frac{1}{4}\), then V(X) is ________

V(4X + 3) is _________

μ₂ = 20, μ¹₂ = 276 for a discrete random variable X. Then the mean of the random variable. X is _________

Variance of the random variable. X is 4, Its mean is 2. Then E(X²) is _________

X is a random variable. Taking the values 3, 4 and 12 with probabilities \(\frac{1}{3},\frac{1}{4}\)and \(\frac{5}{12}\).Then E(X) is

Given E(X + c) = 8 and E(X - c) = 12, then the value of c is ___________

X is a discrete random variable. Which take values 0,1,2 and P(X = 0) = \(\frac{144}{169}\), P(X = 1) = \(\frac{1}{169}\), then the value of P(X = 2) is ________

A random variable X has the following probability mass function

Then λ is

A random variable X has the following probability distribution

Then P(1≤X≤4) is

If \(f(x)=\left\{\begin{array}{lc} k x^{2} & 0  if a p.d.f. then the value of k is ___________