A pocket contains three coins, one of which had a head on both sides, while
the other two coins are normal. A coin is chosen at random from the pocket
and tossed three times. Find the probability of obtaining three heads.
Assume that X is a continuous random variable with pdf f (x) = exp[−(x
+ 2)] if −2 < x < ∞ and zero otherwise. Find E(X) and Var(X) .
If X has a Poisson distribution and if P(X = 0) = 0.2 , find P(X > 4) .
( ln0.2 = −1.60944 )
Suppose that X and Y are discrete random variables with joint pdf of the
form f (x, y) = κ ⋅ (x + y) , x = 0,1, 2 ; y = 0,1, 2 and zero otherwise. Find
the constant κ .
Let X be a random variable that is uniformly distributed, X ~UNIF(0,1) .
Determine the pdf of the random variables Y = e−X and W = X1 / 4 .
Assume that the random variable X ~ N(μ ,σ 2 = 40,000) . Find the
probability of a Type II error when testing the null hypothesis H0 : μ =
1,000 at the α = 0.05 level if the true population mean is μ = 1,200.
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