Question

1- True or false section Write down the question AND the answer in your answer booklet) a. The expected value of a product of two independent random variables is E(XY) EQEY ipt b. A continuous random variable is a random variable that can assume only countable values cThe slope of CDF of any RV could not have negative values. d The expectation fa randomvariable uniformiydistributedover (-2,8)s equalto5__ It e If a and b are constants and X is a random variable , then Var(aX+b)- a'Var(X)+b1pt. Ipt ipt )11pt. (一) TwO events A and B are said to be independentifP(A and B)= P(A)+P(B) If two events are mutually exclusive, they are also independent L İfthecovarianceoftworandomvariablessnegativethis meansthey areuncorrelated.-1( i Tickets numbered from 1 to 20 are mixed up and then a ticket is drawn at random. The 0 probability that the ticket drawn has a number which is a multiple of 3 or 5 9/20.Ipt Three unbiased coins are tossed. The probability of getting at most two beads is 3/8pt. A basket contains 3 red balls and 5 black balls. The probability of drawing two successive red balls (witbout replacement) is equal to 6/56. If a, b are constants and X is a random variable and Y-aX+b, then fu)-

Answer 1

1. a) True
since Independent random variable

b) False
Since continous random variable is a random variable that can infinite countable values

c) True
since CDF is non decreasing function

d) False
since Mean = (-2+8)/2 = 3

e) False
since Var(aX+b) = a^2 Var(X)

f) False
since P(A and B) = P(A) P(B)

g) False

h) False

i) True
since
P(Multiple of 3 or 5) = P(multiple of 3) + P(multiple of 5) - P(multiple of 3 and 5)
= 6/20 + 4/20 -1/20 = 9/20
j) Fasle
since
P(At most 2 heads) = 7/8

k) True
since 3/8 * 2/7 = 6/56

l) True