The rating stress, X, of a Viking hammer, has the following cumulative distribution function F: F(x) = 0 for…

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The rating stress, X, of a Viking hammer, has the following cumulative distribution function F:

F(x) = 0 for x < 0 and F(x)= x² for 0 ≤ x ≤ 4 and F(x):
= 1 for x > 4

16

a) What is the probability density function for X for 0 ≤ x ≤ 4?

O f(x) = 2.x

○ f(x) = x²

O f(x) = x²

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Of(x) = 2-x-8

Of(x) =

b) What is the probability that X > 2.5?

c) What is the probability X < 2.5?
d) What is the probability that X > 3?

e) What is the probability that X > 3.5 ?

f) What is the probability that X > 3.5 given that X > 3?

g) Calculate the median of X.

h) Calculate the expected value of X?

i) Calculate the expected value of x²?

j) Calculate the variance of X?

k) What is the probability that X is more than 0.2 below its expected value?

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Let s go through each of these questions step by step 2 What is the probability density function for X for 0 x 4 In this range 0 x 4 the cumulative di

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