Math Answers

Let X be random variable with the probability density function

fn(x) ={cxⁿ(1−xⁿ) , 0≤x≤1

{0, otherwise.

1) Find the value of c.

2) Determine E[X] .

3) What happens to E[X] for large n?

4) Determine E[X²]

5)What happens to E[X²] for large n?

6)What happens to Var(X) for large n?

If the partition P2 is a refinement of the partition P1 of [a,b], then L(P1,f)≤L(P2,f) and U(P2,f)≤U(P1,f). Verify this result for the function f(x)= 4 cosx , defined over [0, π/2] and for the partition P1= { 0, π/6, π/2} and P2= {0, π/6,π/3,π/2}

. Suppose two medical doctors, A and B, test all patients coming into a clinic for cancer. Let events A+ = {doctor A makes a positive diagnosis} and B+ = {doctor B makes a positive diagnosis}. Suppose doctor A diagnoses 15% of all patients as positive, doctor B diagnoses 23% of all patients as positive, and both doctors diagnose 8% of all patients as positive. a) What is the probability that either doctor A or B makes a positive diagnosis? b) What is the probability that doctor B makes a positive diagnosis of cancer given that doctor A makes a positive diagnosis?

Rina is healthy when, in fact she failed in medical test.

A. Type I

B. Type II

C. Both A and B

D. None of the above