Answer: E(Y) = 1.6 and Var(Y)=1.12
Step-by-step explanation:
Since we have given that
X 0 1 2
P(X) 0.4 0.4 0.2
Here, number of games = 2
So,
Since are independent variables.
so,
So, we get that
So, E[y]=2×0.8=1.6
and Var[y]=2×0.56=1.12
Hence, E(Y) = 1.6 and Var(Y)=1.12
Felecia's husband will catch up to her 1 hour 30 minutes after leaving.
Step-by-step explanation:
Step 1; Felecia is traveling at 45 mph, her husband starts 20 minutes after her but travels at a speed of 55 mph. So first we need to calculate how much of a head start Felecia got.
Head start = × 45 miles an hour = 15 miles.
So Felecia got a head start of 15 miles.
Step 2; Since Felecia and her husband are traveling at different rates, we can determine how much distance there is between them. Since Felecia is traveling at 45 mph and her husband is traveling at 55 mph, their gap in between is closing at a rate of 55 - 45 = 10 miles every hour. So for every hour, the gap between them is closing by 10 miles.
Total gap initially = 15 miles.
The rate at which gap is being closed = 10 miles an hour.
Time to close the gap = 15 / 10 = 1.5 hours.