Let X be a random variable that is equal to the number of times a 5 is rolled in three rolls of a fair 5-sided die with the integers 1 through 5 on the sides. What is E[X2 ]? What is E2 [X], that is, (E[X])2 ? Justify your answers briefly.

Step-by-step explanation:

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

Firstly we will make PMF

For X=0, P=(4/5)^3=64/125

For X=1, P=C(3,1)*(1/5)*(4/5)^2=3*16/125=48/125

For X=2, P=C(3,2)*(1/5)^2*(4/5)=3*4/125=12/125

For X=3, P=C(3,3)*(1/5)^3=1/125

So,

E[X^2]=1*48/125+2^2*(12/125)+3^2/125=0.84

E[X]=48/125+12/125*2+1/125*3=0.6

So,

E[X]^2=0.36

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.

1) is right

step-by-step explanation: