A graduate student has variable income from his assistance ship and tutoring work. He extimates his monthly income (as of the beginning of the month) to follow follow this distribution:
|
Income
|
Probability
|
|
$850
|
0.35
|
|
$900
|
0.25
|
|
$950
|
0.25
|
|
$1,000
|
0.15
|
His monthly expenses are expected to range from $850 to $1,200, following a uniform distribution.
He has a beginning cash balance in September of $1,500.
1. What is his expected cash balance at the end of the following May?
2. What is the probability that his balance will be negative in one or more month?
3. What is the probability that his May ending balance is less than $500?