Find the quantile function F^(-1)(p) (if one exists) of F(x) = {0 for x<= 0, (1/9)x^2 for 0<x<=3, 1 for x>3. For this, set the CDF equal to p and solve for x. This x is then F^(-1)(p).
Find the quantile function F^(-1)(p) (if one exists) of F(x) = {0 for x<= 0, (1/9)x^2...
Q3. Find the quantile function F-1 for F(x)-1-x-α, x 〉 1
Let X ~ Unif(0,1). Find a function of X that has CDF F(x) = 1 ̶ x ̶ p for p > 0 (this is the Pareto distribution).
f(x) = 3x, 0<x<1 0, otherwise Problem 9: Find the CDF of X, [4] Problem 10: Find P(X < 1/3) [4] Problem 11: Find the 95th percentile of X (Remark: You have to solve for x in the equation P(X < x) = .95) [4] Problem 12: Find P(X > 2/3|X > 1/3) [4] A pipe-smoking Mathematician carries two match boxes, box A in his left hand and box B in right-hand pocket. Initially, each box contains 3 matches. Each...
Additional Problem 4. We say that mp is the pth quantile of the distribution function F if F(mp) = p, 0<p<1. Find mp for the distribution having the following density functions: (a) f(x) = 5e*r, x > 0. (b) f(x) = ir', 0 < x < 2. -1<r1
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.
2. Suppose that the CDF of X is given by Fur :53 e-3 for x <3 Fx)for 3 for r >3. 1 (a) Find the PDF of X and specify the support of X. (b) Given a standard uniform random variable U ~ uniform(0, 1), find a transformation g) so that X g(U) has the above CDF. (Hint: This entails the quantile function F-().)
2. Suppose that the CDF of X is given by Fur :53 e-3 for x 3....
Q3. Find the quantile function F-1 for F(r)-1-1-α, x > 1.
i need F and C please
Definitions (different from text) • The p quantile (or (100p) percentile) of the distribution of X is the smallest x such that PIX S x) 2 p. Use zp(x) to denote the p quantile. 2.50(X) is the median of the distribution of X. 15. Find the quantile of order po < p < 1) for the following distributions. (a) f(x) = 1/x2, x 2 1, and zero elsewhere. (b) f(x) = 2x exp(-x2), x...
Consider the function f(x) = 1/6 for 0 ≤ x ≤ 9. Find P(1.5<x<6.25).
5. A function f has Taylor series (at 0) f(x)=0+2x+ 4x2/2! + 3x3/3!+... Assume f−1 exists. Find as much of the Taylor series of f−1 (at 0) as you can. (Since you only know the first few terms of the Taylor series for f, you can only figure out f−1. (Hint: There are two ways of doing this problem. One is get the derivatives of f−1 from knowing the derivatives of f; we talked about the first derivative in January...