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)

Which command will calculate P(X>1.2) when X∼N(3,4)?

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

Let 𝑋X be a continuous random variable with the following PDF:𝑓𝑋(𝑥)={𝑥1(4𝑥2+3𝑥−2)0<𝑥≤10otherwisef X​ (x)={ x 1 (4x 2 +3x−2)0​ 0<x≤1otherwise​ Find the value of 9𝐸[𝑋].E[X].Enter your answer correct to two decimals accuracy.

Let X be a discrete random variable with the following PMF:PX (x) =0.1 for x = 0.20.2 for x = 0.40.2 for x = 0.50.3 for x = 0.80.2 for x = 10 otherwise(a) Find RX , the range of the random variable X.(b) Find P (X ≤ 0.5).(c) Find P (0.25 < X < 0.75).(d) Find P (X = 0.2 | X < 0.6).

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)