Question 5 6 pts consider a condnuous random vanablc D whose pdf tunction f(x)-I

Question

Question 5 6 pts consider a condnuous random vanablc D whose pdf tunction f(x)-Ikx2.HOSK 4, where k is a constant. Find the vleofk Question 6 6 pts Consider a continucus random variable D hoe f unction i 0 otherwise Enter a formula for the cmt F [ on the intorval Osxs4 Question7 6 pts consider a continuous random vanablc D whose pdf tunction f(x)-Ikx2.HOSK 4, where k is a constant. Find P D 21. Question 8 6 pts Cansider a continucus random variable Dwhodf function i 0, athewiee where kis a constant. Find median of D Question 9 6 pts Consider a condnucus random variable D whoc pat function where kis a constant Find E(D Question 10 6 pts Consider a continucus random variable D whose pt function i 0, otherwie where kis a constant. Find E (D2

Explanation / Answer

Please post 1 question per post, here' the answer to the 1st question:

5.

f(x) = kx^2, if 0<=x<=4
= 0, otherwise

The total area of this function from 0 to 4 is 1

Integrating the function f(x) w.r.t to x, we have:

kx^3/3 +c from 0 to 4 is 1

k(64-1)/3 + c-c = 1

k = 1/21

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