Below is the graph of the pdf for a random variable X.  What is 𝑃(X ≤ 3.4)? Round to 3 decimal places.

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.

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

Let 𝑍 be a standard normal random variable. Use the Standard Normal Distribution Table in Learn to find the probability below to four decimal places.

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)

Suppose X is a continuous random variable with the following probability density func-tion:f (x) = c(2 − x), 0 ≤ x ≤ 2(a) [2 marks] Plot the probability density function, clearly marking on your plot thevalues of f (x) when x = 0 and x = 2 and labelling both axes.(b) [2 marks] Explain and show why the value of c must equal 12 .(c) [2 marks] Find P (1 < X < 1.5).(d) [3 marks] Find P ({1 < X < 1.5}|{X > 0.5}).(e) [2 marks] Find P ({X > 0.5}|{1 < X < 1.5}).(f) [4 marks] Suppose that we have another random variable U that is uniformlydistributed with parameters 2 and 4. That is, the probability density function of Uis given byf (u) = 12, 2 ≤ u ≤ 4.Further, U and X are independent. In addition, someone has told us that therandom variable Y defined byY = X + Uhas expected value equal to 113 and variance equal to 59 . Based on this information,calculate the expected value and variance of X