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The moment generating function (mgf) of y is given by
Since the momoent generating function of x is given by
When p tends to 0, we have
Applying L'Hopital's rule we have:
This shows that y converges to <span>a chi squared random variable with 2r degrees of freedom</span>.
Since the momoent generating function of x is given by
When p tends to 0, we have
Applying L'Hopital's rule we have:
This shows that y converges to <span>a chi squared random variable with 2r degrees of freedom</span>.
Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.
Step-by-step explanation:
The given is,
Investment = $ 8000
No. of years = 15 years
Interest rate, i = 3.1 %
( compounded monthly )
Step:1
For for calculating future value with compound interest monthly,
.................(1)
Where,
A = Future amount
P = Initial investment
r = Rate of interest
n = Number of compounding in a year
t = Time period
Step:2
From given values,
P = $8000
r = 3.1%
t = 15 years
n = 12 ( for monthly)
Equation (1) becomes,
A = $ 12728.48
Result:
Dave will have $12,728 after 15 years, if he has $8000 to invest for 15 years. He finds a bank that offers an interest rate of 3.1% compounded monthly.