Find Rx, the range of the random variable X. b. Find P (X≤0.50). c. Find P (0.25 < X < 0.75). d. Find P (X = 0.20 | X<.060).
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Let X be a discrete random variable with the following PMF
PX(x) = 0.10 for x = 0.20
= 0.20 for x = 0.40
= 0.20 for x = 0.50
= 0.30 for x = 0.80
= 0.20 for x = 1.00
= 0.00 otherwise
a. Find Rx, the range of the random variable X.
b. Find P (X≤0.50).
c. Find P (0.25 < X < 0.75).
d. Find P (X = 0.20 | X<.060).
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- The marginal distributions of two random variables X and Y, together with some values of their joint distribution, are given in the table below. Fill in the table in such a way that X and Y are independent random variables. Y= -2 Y= 0 Y= 3 X= -3 0.02 0.03 0.05 0.10 X=0 0.21 0.70 X= 3 0.06 0.20 0.20 0.30 0.50 1.00Let T be a random variable. If E(T) = a +60, find an unbiased estimator of 0. Is the mean- squared error (MSE) of an unbiased estimator always smaller than the MSE of a biased estimator? Give an example to support your answer.Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal with a mean u= 7500 and a = 1750. A test result of x < 3500 is an indication of leucopenia. This indicates bone marrow depression that may result in a viral infection. a. What is the probability that on a single test x is less than 3500? b. A patient is given 3 tests at regular intervals. What is the probability that the average of the three tests is less than 3500?
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