# Question: With reference to Exercise 6 17 using the fact that the

With reference to Exercise 6.17, using the fact that the moments of Y about the origin are the corresponding moments of X about the mean, find a3 and a4 for the exponential distribution with the parameter θ.

In exercise

If X is a random variable having an exponential distribution with the parameter θ, use Theorems 4.10 on page 128 and 6.4 to find the moment- generating function of the random variable Y = X – θ.

In exercise

If X is a random variable having an exponential distribution with the parameter θ, use Theorems 4.10 on page 128 and 6.4 to find the moment- generating function of the random variable Y = X – θ.

## Answer to relevant Questions

Show that if v > 2, the chi-square distribution has a relative maximum at x = v – 2. What happens when v = 2 or 0 < v < 2? Verify that the integral of the beta density from – ∞ to ∞ equals 1 for (a) α = 2 and β = 4; (b) α = 3 and β = 3. Show that the normal distribution has (a) A relative maximum at x = µ; (b) Inflection points at x = µ – σ and x = µ + σ. With reference to Exercise 6.39, show that for nor–mal distributions k2= σ2 and all other cumulants are zero. In exercise If we let KX(t) = lnMX – µ(t), the coefficient of tr/r! in the Maclaurin’s series of KX(t) is ...In certain experiments, the error made in determining the density of a substance is a random variable having a uniform density with α = – 0.015 and β = 0.015. Find the probabilities that such an error will (a) Be ...Post your question