xample: A continuous random Variable x has X70 fx(x)= 120 0 Find the E(X). -ax X40 probability density given by [6] 1
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![Example: A continuous random Variable x has
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X70
£260
0
Find the E(X).
fx (x)=
-ax
X40
probability density given by
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- If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2The density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).
- Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.X1 and X2 are independent random variables such that Xi has PDF fXi(x)={λiexp(−λix) when x≥0, 0 otherwise}. What is P[X2<X1]?If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.
- Let X1 and X2 be two continuous random variableshaving the joint probability density f(x1, x2) = 4x1x2 for 0 < x1 < 1, 0 < x2 < 10 elsewhereFind the joint probability density of Y1 = X21 and Y2 = X1X2.A simple random sample X1, …, Xn is drawn from a population, and the quantities ln X1, …, ln Xn are plotted on a normal probability plot. The points approximately follow a straight line. True or false: a) X1, …, Xn come from a population that is approximately lognormal. b) X1, …, Xn come from a population that is approximately normal. c) ln X1, …, ln Xn come from a population that is approximately lognormal. d) ln X1, …, ln Xn come from a population that is approximately normal.Suppose that the continuous random variable X has cumulative distribution function given by F(x)= 0, if x < sqrt(2); x2-2, if sqrt(2) <= x <= sqrt(3); 1, if sqrt(3) <= x Find the probability density function of X.
- A continuous random Variable X has probability Density function defined by f(x) = 5-5x; 0If two random variables X1 and X2 have the joint density function given by f (x1, x2) = x1x2, 0 < x1 < 1, 0 < x2 < 2 0, otherwise Find the probability that (a) Both random variables will take on values less than 1 (b) The sum of the values taken on by the two random variables will be less than 1.Suppose that X is a random variable with density and suppose that ?=e(-4X) Determine ?(?)
