Expected value of f(x) must equal 2
The integral of f(x) from a to b must equal 1 to satisfy PDF
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Find a function f(x) for a≤x≤b (and zero elsewhere) such that f(x) is a PDF of a continuous random variable and μ = 2
Give a function f(x)f(x) for a≤x≤ba≤x≤b (and zero elsewhere) such that ff is a PDF of a continuous random variable with expected value μ=7μ=7. Give a function f(c) for a < < < b (and zero elsewhere) such that f is a PDF of a continuous random variable with expected value u = 7. f(x) = , for
(a) Let X be a continuous random variable with the cdf F(x) and pdf f(.1). Find the cdf and pdf of |X|. (b) Let Z ~ N(0,1), find the cdf and pdf of |Z| (express the cdf using ” (-), the cdf of Z; give the explicit formula for the pdf).
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Let X be a continuous random variable with pdf ( cx?, |a| 51, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Let X be a continuous random variable with pdf ( cx?, [xl < 1, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
(b) Let X be a continuous random variable with pdf given by: f(x) =c#x Find the constant c so that f(x) is a pdf of a random variable. C (ii) Find the distribution function F(x)P(X Sx)X (ii) Find the mean and variance of X. .Col니loa, ,iaaa4
X is a continuous random variable, f(x) is the probability density function (pdf) of X, and F(x) is the cumulative distribution function of X. Then for any two numbers a and b with a < b, which of the following are true? Circle all correct answers. A. B. C. D. 5. If X is a normally distributed random variable with a mean of 36 and a standard deviation of 12, then the probability that X exceeds 36 is: A. .5000...
2. Suppose that the continuous random variable X has the pdf f(x) = cx3:0 < x < 2 (a) Find the value of the constant c so that this is a valid pdf. (10 pts) (b) Find P(X -1.5) (5 pts) (c) Find the edf of X use the c that you found in (a). (Hint: it should include three parts: x x < 2, and:2 2) (20 pts) 0,0 <
2. Let X be a continuous random variable with pdf ca2, 1 f(x) otherwise, where the parameter c is constant (with respect to x) (a) Find the constant c (b) Compute the cumulative distribution function F(x) of X (c) Use F(x) (from b) to determine P(X 1/2) (d) Find E(X) and V(X)
a) The pdf of a random variable X is (1-μ e 26 The generating function of X is t2 -2 Use what you see to write down the Fourier transform of pdf[x] b) What is the relation between The Fourier transform of pdf[x] and the characteristic function of X? c) If the pdfs of two random variables have the same Fourier transform, then must they have the same cumulative distribution function? L.14 The pdf of a random variable X is...