Probability and statistics involving continuous pdfs and integration. Just 3 questions. Could it be done today?

57558 Assignment
Q.No.1
Given pdf when we integrate we get
So it cannot be a valid pdf. For a valid pdf, total integral should come to 1.
So I make pdf of X as
When x<=0, y = -x In other words y can be positive only.
If x is positive y = x^2 again positive
So y takes values from 0 to 4.
A) f(y) = 2/15 (x+2) =
=
B) E(y) = + +0.8583=0.9472
C) E(y) using f(x) = 0.1777+
So E(y) = 0.9472
QNo.2
P(sick) = P(H’) = 0.02 and P(H) = 0.98
A) pdf for healthy persons = and
pdf for sick persons = 0.02
B) f(x) = I+II =0.02
C)
Prob for both T negative and healthy is the test result declaring a healthy person as sick. i.e. P(X≤70) for a healthy person
= P(Z≤(50-70/20) )...