Additional Problem 4. We say that mp is the pth quantile of the distribution function F...
show steps, thanks » Additional Problem 4. We say that mp is the pth quantile of the distribution function F if Find m, for the distribution having the following density functions: (a) f(z) = 5e-5e, X 〉 0 (b) f(z) = 3, 0 〈 x 〈 2. (c) f(x) =ー2ー r+1 ,一1 < x 〈 1. Answers: (a) -r In (1-p), (b) 2p1/4, (c)-1 +2, P » Additional Problem 5. Suppose that X is equally likely to take any of...
Additional Problem 3. If X is a continuous random variable having cdf F, then its median is defined as that value of m for which F(m) = 0.5. Find the median for random variables with the following density functions (a) f(r)-e*, x > 0 (c) f(x) 6r(1-x), 1. Additional Problem 6. Let X be a continuous random variable with pdf (a) Compute E(X), the mean of X (b) Compute Var(X), the variance of X. (c) Find an expression for Fx(r),...
show steps thank you . Additional Problem 6. Let X be a continuous random variable with pdf f(x) = (z + 1), -1 x 2. (a) Compute E(X), the mean of X. (b) Compute Var(X), the variance of X (c) Find an expression for Fx(), the edf of X. (d) Calculate P(X > 0). (e) Compute the mean of Y, where Y (f) Find mp, the pth quantile of X X-1 X+1
Additional Problem 3. If X is a continuous random variable having cdf F, then its median is defined as that value of m for which F(m) = 0.5. Find the median for random variables with the following density functions (a) f(r)-e*, x > 0 (c) f(x) 6r(1-x), 1.
1.For x ≥ 0, let f(x) = 2xe−x^2 Show that f is a density function. 2. Find the cumulative distribution for the density in the preceding exercise. 3. Find the pth quantile of this distribution.
Q3. Find the quantile function F-1 for F(r)-1-1-α, x > 1.
Problem 1-5 1. If X has distribution function F, what is the distribution function of e*? 2. What is the density function of eX in terms of the densitv function of X? 3. For a nonnegative integer-valued random variable X show that 4. A heads or two consecutive tails occur. Find the expected number of flips. coin comes up heads with probability p. It is flipped until two consecutive 5. Suppose that PX- a p, P X b 1-p, a...
(+3) The pdf f(x) of a random variable X is given by 0, ifx<0 Find the cumulative distribution function F(r
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.