4. Let X be a continuous random variable defined on the interval [1, 10 with probability...
3. Let X be a continuous random variable defined on the interval 0, 4] with probability density function p(r) e(1 +4) (a) Find the value of c such that p(x) is a valid probability density function b) Find the probability that X is greater than 3 (c) If X is greater than 1, find the probability X is greater than 2 d) What is the probability that X is less than some number a, assuing 0<a<4?
Let X be a continuous random variable defined on the interval [0, 4] with probability density function p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. (d) What is the probability that X is less than some number a, assuming 0 < a <...
That is a PLUS sign in the equation. Let X be a continuous random variable defined on the interval [0, 4] with probability density function p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. (d) What is the probability that X is less than...
3.98 Let X be a continuous random variable with probability density function f(x) defined on = {xl-π/2 < x < π/2). Give an expression for VIsinX)
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
7, Let X be a continuous random variable with probability density function: 0, f x<0 150 f x> 10 ind ihe avnanted value and mode of random variable X
Let X be a uniformly distributed continuous random variable that lies between 1 and 10. i. Sketch the probability density function for X. ii. Find the formula for the cumulative distribution for X and use it to compute the probability that X is less than 6
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
Find the variance of random variable X. 7.. Let X be a continuous random variable whose probability density function is: -(2x3 + ar', if x E (0:1) if x (0;1) Find 1) the coefficient a; 2) P(O.5eX<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given X 8 -2 0 2 8
1. (10 points) Let X be a continuous random variable with the probability density function given by f(x)-4z if 0SaS1 and O otherwise (a) Find P(X sjIx> j) (b) Find the expectation and variance of X