1. Let X represent the number of times your professor goes to the gym
each week. You are given the following probability table for X.
Unfortunately, your professor spilled some coffee on the probability
for x = 5 and it is now illegible.
x 1 2 3 4 5
P(X = x) 0.12 0.25 0.38 0.17 ???
(a) What is P(X = 5)?
All the probabilities must add up to 1, the probability of certainty,
because it is certain that one of them will occur.
So add 0.12 + 0.25 + 0.38 + 0.17 and get 0.92
Then subtract 1.00 - 0.92, and get 0.08
So now we know that what he spilled coffee on was 0.08
x 1 2 3 4 5
P(X = x) 0.12 0.25 0.38 0.17 0.08
(b) Find the expected value of X.
Multiply each x by the corresponding probability P(X=x) and add:
E(X) = 1×0.12 + 2×0.25 + 3×0.38 + 4×0.17 + 5×0.08 = 2.84
(c) Find the standard deviation of X.
E(X) = 2.84
E(X²) = 1²×0.12 + 2²×0.25 + 3²×0.38 + 4²×0.17 + 5²×0.08 = 9.26
Edwin
