Let n39 and 5 afind px 2b find p1 y 3cfind px 4y

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Problem 2 [18 points]. Let ?~N(3,9)and ? = 5 − ?a)Find P(X > 2)b)Find P(−1 < Y < 3)c)Find P(X > 4|Y < 2)Please use an approximation to calculate the value of Φ(x), where necessary. . 3)Further, we can approximate Φ(x)using: for all ? ∈ ℝ
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Page 3 of 8 Problem 3 [24 points]. A continuous random variable Z is said to have a 𝐿?𝑝𝑙???(𝜇, ?)distribution if its PDF is given by: ??(?) =12??|?−𝜇|𝑏where 𝜇 ∈ ℝand ? > 0a)If X ~ 𝐿?𝑝𝑙???(𝜇 = 0, ? = 1), find E[?]and Var[?]b)If X ~ 𝐿?𝑝𝑙???(𝜇 = 0, ? = 1)and ? = ?? + 𝜇, show that Yis a Laplace random variable.c)Let Z ~ 𝐿?𝑝𝑙???(𝜇, ?), where 𝜇 ∈ ℝand ? > 0. Find E[?]and Var[?] . . . .
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