A discrete random variable X has the probability distribution shown in the table belowDetermine the value of the constant a

A discrete random variable X has this probability distribution.a) Complete the table (10 pts)Compute:b) 𝜇 = 𝐸(𝑋) = ∑[𝑥𝑃(𝑥)] = ___________________ (2 points)c) 𝑉𝑎𝑟(𝑋) = ∑[(𝑥 − 𝜇)2𝑃(𝑥)] = ___________________ (2 points)d) Standard deviation. ___________________ (1 points)Note: Answers from b – d, round off to 2 decimal places. For the table take all decimal places.𝑥 0 1 2 3 4𝑃(𝑥) 0.12 0.25 0.18 0.35 0.10𝑥𝑃(𝑥)𝑥 − 𝜇(𝑥 − 𝜇)2(𝑥 − 𝜇)2𝑃(𝑥)

Given the following discrete probability distribution of the discrete random variable Z:

A discrete random variable X can only assume the values of 0, 1, 2 and 3.Given that 𝑃(𝑋 ≥ 2) = 0.6 , 𝑃(𝑋 ≤ 2) = 0.85Determine 𝑃(𝑋 = 2)

If X is a continuous random variable, then =P=Xa ▼(Choose one) for any number a.

What is the expected value of the probability distribution of the discrete random variable X?x P(X = x)2 .074 .196 .258 .1110 .0712 .3014 .01