Calculating Probability DensityIn a uniform PDF, all the possible values have the same probability density. The figure below shows such a uniform PDF, where the possible values are from 0 to 10. For this graph, what is the value of the probability density from X = 0 to X = 10?

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

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

For Continuous Probability Distribution, the area under the curve represents probability. What is the maximum value of probability? Question 1 options: 0.10 0.75 10.00 0.50 1.00

The Probability density function for a continuous random variable X is given by 𝑓(𝑥)=𝑥34 for 0<x<2 and 0 elsewhere. What is the cumulative distribution function of X?

Suppose that the random variable X is continuous and takes its values uniformly over the interval from 0 to 2. What is the value of the probability P{X ≤ 0.4 or X > 1.2}?