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Suppose that the probabilities of events A and B are P(A)=.4, and P(B)=.5. If A and B are independent events, then P(B|A) is equal to O.4 O .5 O Cannot be determined Suppose that you have a loaded die, where the probability of landing on each number is given by the following: X 3 6 P(X=X) 0.3 0.1 0.1 0.1 0.1 .3 Find the expected value of a single roll of the die. O1 O 21 O 3.5 O 3 Suppose that you have a loaded die, where the probability of landing on each number is given by the following: 3 5 6 P(X=X) 0.3 0.1 10.1 0.1 0.1 .3 Find the standard deviation of a single roll of the die. O 2.06 4.25 O 1.06 O 3.5 Suppose that all of the outcomes of a random variable are (a, b, c, d, e }, and that P(a)=P(b)=P(c)=P(d)= 1/4, (that is, all outcomes a, b, c, and d each have a 1/4 probability of occuring), and P(e)=0. Define the events A= (a,b), B= (b.c), C= (c,d), and D=(e ) . True or false: The events A and B are independent. True O False Suppose that all of the outcomes of a random variable are {a, b, c. d, e ) , and that P(a)=P(b)=P(c)=P(d)= 1/4, (that is, all outcomes a, b, c, and d each have a 1/4 probability of occurring), and P(e)=0. Define the events A= (a,b), B= (b,c), C= (c.d), and D= (e ). Calculate the probability PIA|C). O 1/2 O 1/8 O 1/3