# Question: The logarithm of the ratio of the output to the

The logarithm of the ratio of the output to the input current of a transistor is called its current gain. If current gain measurements made on a certain transistor are normally distributed with µ = 1.8 and σ = 0.05, find the probability that the current gain will exceed the required minimum value of 6.0.

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If the joint density of X and Y is given by And Z = X + Y / 2 , find the probability density of Z by the distribution function technique. Explain the results of Exercise 5.28 on page 164 in light of Theorem 8.6. Prove Theorem 8.9. Theorem 8.9 If X1, X2, . . . , Xn are independent random variables having chi- square distributions with v1, v2, . . . , vn degrees of freedom, then Has the chi-square distribution with v1 + v2 + · · · ...Use the results of Exercises 8.25 and 8.27 to show that if X has a chi-square distribution with v degrees of freedom, then for large v the distribution of √2X – √2v can be approximated with the standard normal ...If X has an F distribution with v1 and v2 degrees of freedom, show that Y = 1/X has an F distribution with v2 and v1 degrees of freedom.Post your question