1.A machine produces copper wire, and occasionally there is a flaw at some point along the wire. The length of wire produced between successive flaws is a continuous random variable X with pdf of the form f(x) = { S(1 +x)°,x>0 a) Find the constant e? b) Find the cumulative distribution function of X? c) Find P(0.40s X s 0.45)?

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A: The given moment generating function of a random variable X is 13+23et5.

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Q: Suppose that Y is an exponential random variable with λ = 4. Find. P[Y > (E(Y) + 2√√Var(Y))].

A: From given data we have : λ=4 and Y~exp(λ)

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.