The diameter of a rivet (in mm) is a random variable with probability density function ?(?) = { 3 4 (? − 9)(11 − ?) 9 < ? ≤ 11 0 ??ℎ?????? }
a. find the cumulative distribution function of the diameter
b. the specification of the diameter is 9.4 to 10.2. what is the probability the specification is met
The diameter of a rivet (in mm) is a random variable with probability density function ?(?)...
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
Suppose density function positively valued continuous random variable X has the probability a fx(x)kexp 20 fixed 0> 0 for 0 o0, some k > 0 and for (a) Find k such that f(x) satisfies the conditions for a probability density function (4 marks) (b) Derive expressions for E[X] and Var[X (c) Express the cumulative distribution function Fx(r) in terms of P(), the stan dard Normal cumulative distribution function (8 marks) (8 marks) (al) Derive the probability density function of Y...
Question 3 (10 point) The error in the length of a part (absolute value of the difference between the actual length and the target length), in mm, is a random variable with probability density function 0 otherwise a. Find the cumulative distribution function of the error b. What is the probability that the error is less than 0.2 mm? c. Find the mean error d. Find the variance of the error. e. The specification for the error is 0 to...
9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...
The random variable X has probability density function f (x) = k(−x²+5x−4) 1 ≤ x ≤ 4 or =0 1 Show that k = 2/9 Find 2 E(X), 3 the mode of X, 4 the cumulative distribution function F(X) for all x. 5 Evaluate P(X ≤ 2.5). 6 Deduce the value of the median and comment on the shape of the distribution.
4. (30pts) A continuous random variable X has the probability density function: hx - 1 sx 32 f(x) =Jo-hx 2 x 3 0 x >3 which ean bo graphed as f(x) 1 2 a) Find h which makes f(x) a valid probability density function b) Find the expected value E(X) of the probability density function f(x) c) Find the cumulative distribution function F(x). Show all you work
6. Let X be a continuous random variable whose probability density function is: 0, x <0, x20.5 Find the median un the mode. 7. Let X be a continuous random variable whose cumulative distribution function is: F(x) = 0.1x, ja 0S$s10, Find 1) the densitv function of random variable U-12-X. 0, ja x<0, I, ja x>10.
(a)The continuous random variable X is distributed with probability density function f defined by f(x) = (1/64)x * (16 - x^2) , for 0 < x < 4. . Find [V (2x+1)] . (b) -An urn contains 7 white balls and 3 black balls. Two balls are selected at random without replacement. What is the probability that: 1-The first ball is black and the second ball is white. 2-One ball is white and the other is black ( C)- Suppose...
2x 0<x<1 Let X be a continuous random variable with probability density function f(x)= To else The cumulative distribution function is F(x). Find EX.