Reference no: EM132589796

Assignment - Random Variables

Discrete RV - Example 1

A box contains four chips. Two are labeled with the number 2, one is labeled with a 4 and the other with an 8. Let X be the label of a randomly selected chip. Find E[X] and var[X].

Discrete RV - Example 2

A discrete RV X has a PMF of the form p(x) = c(8 - x) for 0 ≤ x ≤ 5 and zero otherwise. Find (i) the constant c, (ii) the CDF, F(x) (iii) P (X > 2) (iv) E[X].

Discrete RV - Example 2 (BE 2.7)

A discrete RV X has a PMF of the form p(x) = c(8 - x) for 0 ≤ x ≤ 5 and zero otherwise. Find (i) the constant c, (ii) the CDF, F (x) (iii) P(X > 2) (iv) E[X].

Discrete RV - Example 3 (advance)

Books from a certain publisher contain an average of 1 misprint per page. What is the probability that on at least one page in a 300-page book from this publisher there will be at least 5 misprints?

Continuous RV - Example 1 (HK 5.1-3)

The time, in seconds to compile computer programs written by students in a certain class is a random variable X with probability density function, f(x) = 3/(x + 1)⁴ for x ≥ 0 and zero otherwise. Find (i) the probability that it takes more than 1.5 seconds to compile a program. (ii) the time m at which P (X ≤ m). This value is called the median of the random variable X.

Application: Breast Mammogram X-rays

90% results are "false positives" and 15% are "false negatives" One in nine women will get beast-cancer sometime during their lives.

What is the probability that a random positive test result is actually correct?

A: Has cancer, P (A) = 1/9

B: Test is positive

P (False positive) = P(B|A^c) = 0.9

P (False negative) = P(B^c|A) = 0.15

P (A|B): Positive result is correct.