X is a random variable whose possible values are X = {1, 3, 8}. Suppose that the

Question

X is a random variable whose possible values are X = {1, 3, 8}. Suppose that the probability of each of these values is given by the formula P(X = x) = x/12. For example, P(X = 1) = 1/12. a Calculate the expected value of X. b) Calculate the standard deviation of X. A rare disease has a 1% of prevalence rate. We have a test which is 98% sensitive and 95% specific. a) If we apply the test to an individual and get a positive reading, what is the probability that he has the disease? b) If we apply the test to an individual and get a negative reading, what is the probability that he does not have the disease?

Explanation / Answer

3. a.

In order to find the mean (expectation) of the given distribution, we will use the following formula:

=xp(x)=1*1/12+3*3/12+8*8/12=6.19

b.

In order to find the standard deviation of the given distribution, we will use the following formula:

=(x2p(x)2)

Now we will find the sum:

x2p(x)=1*1/12+9*3/12+64*8/12=45.21

Putting all together we have:

=2.6256

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