
1. A random variable X has the cumulative distribution function exe F(X) = 1 + ex...
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
Exercise 3.37. Suppose random variable X has a cumulative distribution function F(x) = 1+r) 720 x < 0. (a) Find the probability density function of X. (b) Calculate P{2 < X <3}. (c) Calculate E[(1 + x){e-2X].
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2.5.9. The random variable X has a cumulative distribution function 0, forx<0 F(x) for x > 0. for x > , 1+x2" · Find the probability density function of X.
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
(15 points) Let X be a continuous random variable with cumulative distribution function F(x) = 0, r <α Inr, a< x <b 1, b< (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution function F,(x) f()dt of X and Var(X) (c) Let A be any Borel set of R. Define P by P(A) [,f dm
5. (20%) Let X be a continuous random variable whose probability density function is fr(x) (a +bx)%0(x) (a) If Ex)f find a and b. (b) Give the cumulative distribution...
2.5.9. The random variable X has a cumulative distribution function for xo , for xsO . for r>0 F(x) = z? 1 +x2 Find the probability density function of X.
2.5.9. The random variable X has a cumulative distribution function for xo , for xsO . for r>0 F(x) = z? 1 +x2 Find the probability density function of X.
12. (15 points) Let X be a continuous random variable with cumulative distribution function 0, <a F(x) = Inr, asi<b 1, bsa (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(x > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
Question 3: Let X be a continuous random variable with
cumulative distribution function FX (x) = P (X ≤ x). Let Y = FX
(x). Find the probability density function and the cumulative
distribution function of Y .
Question 3: Let X be a continuous random variable with cumulative distribution function FX(x) = P(X-x). Let Y = FX (x). Find the probability density function and the cumulative distribution function of Y