4, (10 points) Use the reflection principle to find the probability P(Ma = 6), where MS-...
DO NOT COPY OTHER ANSEWERS!!!! 2. (10 points) Let (%)n>o be a simple symmetric random walk. Compute P(Sn-y|S,n-x) for the two cases n > m and n < m
Suppose you plan flipping a coin twice where the probability p of heads has the density function f(p) = 6p(1 - p), 0 < p < 1. Let Y denote the number of heads of this “random” coin. Y given a value of p is Binomial with n = 2 and probability of success p. a. Write down the joint density of Y and p. b. Find P(Y = 2). c. If Y = 2, then find the probability that...
Part 4 of 10 - Question 4 of 10 1.0 Points Find k such that Pr[Z<k] = .7517, where Z is the standard normal random variable. O A..2483 O B.-.32 Oc..32 O D.-.68 O E..68 Reset Selection
2. The probability density function of X is given by 10 0,x < 10 a) Find P(X>20). b) What is the cumulative distribution function of X?
SupposeYi,Yexp(e Use the CLT to approximate the following probability P(-1.96 < 1.96)
(10 points) Let Y have probability density function (pdf) 3y?, for ( <y<1 fy(y) = 10, otherwise (a) Compute the probability density function (pdf) of 1/Y. (b) Compute the probability density function (pdf) of Y1 +Y2, if Yį and Y2 are inde- pendent random variables with the same pdf as Y. (You can use a computer to help with the integration).
5. A random variable X follows a binomial distribution with n 35 and p-4. Use the normal approximation to the binomial distribution to find P(X < 16)
Data analysis 5. (10 points) Please determine the following probability given the Z value using the standard normal distribution table a) P(Z < 1.28) b) P(Z>1.45)
0.309 <p <0.391 0.316<p <0.384 0.349<p<0.351 Find the probability P[Z<-0.36) using the standard normal distribution 0.6400 0.8594 0.6406 0.3594 QUESTION 6 If the standard deviation of a normally distributed population is 50.0 and we take a sample of error of the mean is 50.0 10.0 Click Save and Submit toate and subut Clio So t oane
IS Find the following probability for the standard normal random variable z. a. P(z<-1.02) b. P(z <2.03) c. P(0.68 szs2.03) d. P(-2.66szs1.56) a. P(z -1.02)(Round to four decimal places as needed.) b. Pize 2.03)=[] (Round to four decimal places as needed.) ook c. P(0.68 szs2.03) (Round to four decimal places as needed.) d.P(-2.66 s zs 1.56) = [□ (Round to four decimal places as needed.)