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We have a random variable X that is the number of months that a certain owner of an estate needs to pay a loan in the Bank if he/she has a contract with insurance company to help him/her to pay a loan. X's probability mass function is:

$$f(x)=\frac{5-x}{10}, x= 1,2,3,4$$

If the owner receives 200usd from the insurance comp per month for the first 2 months and then 100usd per month after the first 2, what is the expected payment for the loan at the bank?

For this question, I'm having a hard time understanding where I would plug in the 200usd and 100usd, I assume the formula for expected value would be used here but it still does not help me know where to place the amount... Perhaps $$E(X)=\sum xf(x)= 200*x_1*f(x_1) + 200*x_2*f(x_2) + 100*x_3*f(x_3) + 100*x_4*f(x_4) $$??

If I could get a hint for this that would be great!

Thank you

Michael Vie
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  • He pays 200 with a prob. of f(1)=4/10. He pays 400(=200+200) with a prob of f(2)=3/10. And so on. Thus $E(X)=2004/10+4003/10+5002/10+6001/10$ – callculus42 May 17 '22 at 08:47
  • @callculus42 Could you explain to me why it's 400 for the second month since it's 200 per month, I don't understand why we'd add the previous 200 to it – Michael Vie May 17 '22 at 10:14

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