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Let ƒ : R → R an applicationdefined for all x, by:
Where λ € R and µ > 0
1- Determine kas a function of µ such that ƒ is the probability density function of a random variable X.
2- What is the distribution function of X?
3- If we define Y=X-λ/µ. What is the distribution of Y?
4- Calculate E(X) and V(X)
5- Evaluate P (| Y | ≥ 2). Compare with P (| U | ≥ 2) where U successively follows a distribution N (0, 1), a distribution of Student at 20 degrees of freedom, a Cauchy distribution of density ƒ(u)=1/∏(1+x2), a double exponential distribution of density ƒ(x) = exp {-x-e-x}
Determine the sample size necessary to estimate a population mean to within 1 with a 90% confidence given that the population standard deviation is 10.
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Assume that each light bulb works independently of other light bulbs. Determine the probability that all 10 of light bulbs work?
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1. each supplier is rated on a 10-point scale 10 highestfor four different criteria price quality delivery and
What is the probability that the drug will be effective for 2 hours or less?
for the following problems do the followinga draw thenbspscatter plotnbspfor the variables.b compute thenbspcorrelation
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