2) Suppose X is a Normal RV with mean = 17 and variance = 4. Find...
1) Suppose X is a Normal RV with mean = 12 and variance = 16. Find (a) P(X < 14) (b) P(14.5 < X < 18) (c) P(X < 16 or X > 12). Hint: Remember to always identify outcomes of interest first! (d) The center of the probability density function of X.
3) Suppose X is a Normal RV with mean = 17 and variance = 4. Note this is the same random variable as in Question 2. Find (a) P&717<-1.5) (b) P(-1.25 < *=12 <.5) (c) P(+297 < 2)
(20 points) Suppose X~N(25, 81). That is, X has a normal distribution with μ-25 and σ-81 la. Find a transformation of X that will give it a mean of zero and a variance of one (ie., standardize X lb. Find the probability that 18 < χ < 26. lc. Supposing Y10 +5X, find the mean of Y ld. Find the variance ofY
0 x/8 x <0 0 11, Find the mean when F(x) = x < 2
6. Let X be a normal random variable with mean u = 10. What is the standard deviation o if it is known that p (IX – 101 <>) =
1. Using calculus, find the mean and variance of a uniform distribution with a minimum value of of O and a maximum value of 10. (Give a proof.) Remember that the variance can be calculated using: < X z >-< X >2.
If X is a normal rv with mean 85 and standard deviation 20, compute the following probabilities by standardizing. (a) P(X < 125) .9772 (b) P(X < 85) 5 (c) P(55 SX 125) .9104 (d) P(65 < X) .8413 (e) P(95 <x<115) .2417 (f) P( [X - 850 < 20) .7357
(20 points) Suppose X-N(25, 81). That is, has a normal distribution with μ-25 and σ2-81. la. Find a transformation of X that will give it a mean of zero and a variance of one (ie., standardize X). lb. Find the probability that 18<x < 26. 1c. Supposing Y = 10 +5X, find the mean of Y 1d. Find the variance of Y
Suppose that NoP(X5)6 and P(X 2):2 find P( 3< X < 4).
Suppose that the cdf of random variable X is Skex-3, X <4 11, X >4 Find k. (2 Points) Find the expected value of X. (2 Points)