Very lttle is known about the random variable U. It is known, however, that U is a continuous random variable such that...
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.
2. Let U be a continuous random variable with the following probability density function: 1+1 -1 <t<o g(t) = { 1-1 03151 0 otherwise a. Verify that g(t) is indeed a probability density function. [5] b. Compute the expected value, E(U), and variance, V(U), of U. (10)
2. Let U be a continuous random variable with the following probability density function: g(t) = 1+t -1 <t < 0 1-t 0<t<1 0 otherwise a. Verify that g(t) is indeed a probability density function. [5] b. Compute the expected value, E(U), and variance, V(U), of U. (10)
2. Le X be a continuous random variable with the probability density function x+2 18 -2<x<4, zero otherwise. Find the probability distribution of Y-g(X)- XI
2. Le X be a continuous random variable with the probability density function x+2 -2<x<4, zero otherwise. = , Find the probability distribution of Y-g(x)- 12 XI
3) The continuous random variable X has the probability density function, ), 2 3x3 f(x) = { a, 35x55 2 - bx, 5 < x < 6 elsewere 10 i)Find the value of a and b and hence, sketch f(x) ii) Find the cumulative distribution function, f(x) and sketch it.
2. Let U be a continuous random variable with the following probability density function: 1+t g(t) = 1-t -1 < t < 0 0 <t<1 otherwise 0 a. Verify that g(t) is indeed a probability density function. [5] b. Compute the expected value, E(U), and variance, V(U), of U. (10)
Let U be a continuous random variable with the following probability density function: g(t) = 1+t -1<t< 0 1-t 0<t<1 0 otherwise a. Verify that g(t) is indeed a probability density function. [5] b. Compute the expected value, E(U), and variance, V(U), of U. (10)
A random variable is normally distributed with a mean of u = 90 and a standard deviation of o = 10. (a) The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 60 and 120). Areas Under the Curve for any Normal Distribution 99.7% 95.4% + 68.3% – pi - 30 -lo u u + lo u + 30 A...
Let F(u) be the distribution function of a random variable X whose density is symmetric about zero. Show that F(-u)=1-F(u)