. [19 points] Refer to Problem 1. (a) Find the cumulative distribution function F(x). Be sure to write your answer in the appropriate way. [4 points] (b) Find the mean value of X, i. e. find E(X). [4 points] (c) Find the second moment, i. e. find E(X 2 ). [4 points]

Step-by-step explanation:

a) We know that the cummulative distribution function of a continous random variable X is defined as:

given:

hence its cdf will be

b) Mean of X is given as:

c) For second moment

the answer is 200

step-by-step explanation:

the way the question is worded, it seems to imply the $264 interest is simple interest, not compound interest.

the simple interest for 2 years is $264; the simple interest for 1 year is $132.

$132 interest on a $600 investment means an interest rate of (132/600)*100 = 22%.

the value of $200 at 22% interest compounded annually for three years is

200%281.22%29%5e3

the amount of interest is that value, minus the original $200.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47