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

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
16
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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