36. Consider all courtroom trials with a single defendant who is charged with a felony. Suppose

that you are given the following probabilities for

this situation.

Seventy-five percent of the defendants are, in

fact, guilty. Given that the defendant is guilty,

there is a 70 percent chance the jury will convict the person. Given that the defendant is not

guilty, there is a 40 percent chance the jury will

convict the person.

For simplicity, assume that the only options

available to the jury are: to convict or to release

the defendant.

(a) What proportion of the defendants will be

convicted by the jury?

(b) Given that a defendant is convicted, what

is the probability the person is, in fact,

guilty?

(c) What is the probability that the jury will

make a correct decision?

(d) Given that the jury makes an incorrect decision, what is the probability that the decision is to release a guilty person?

37. Recall that a confidence interval is too small if

the number being estimated is larger than every

number in the confidence interval. Similarly, a

confidence interval is too large if the number

being estimated is smaller than every number

in the confidence interval.

Each of four researchers selects a random sample from the same population. Each researcher

calculates a confidence interval for the median

of the population. The intervals are below.

[24, 41], [30, 39], [20, 33], and [35, 45].

Q. # 4 The joint probability mass function of two random variables is P(X - x, Y - y)=k- (x+ pix=1,2,3, y = 0,1,2. Obtain value of & so that above is a proper probability mass function. Construct the table of joint probabilities alongside the marginal probability mass functions. Also obtain conditional probability distribution of X given Y = 0 and compute P(X - 1|Y -0)4. Suppose X and Y are non-negative random variables with joint probability mass function Pr {X = i, Y = j} = cij for 1