Question

3. (15 pointa) A bag contains 7 red marbles and 3 bue marbles Five martle are draw from the beg with placement Consider the random variable R-the number of red marbles selected B-the number of blue marbles selected 7+3= 10 (a) What are the possible values of each of the following discrete random variables? ponsible values of R: possible values of B: possible values of R+ B: (b) Explain why R is a binomial random variable with n=5 and p-0.7. (Ia particular, explain why it is essential that the marbles are drawn with replacement.) (c) Write down the probability distribution of R. You can either use -binondist (1,n.p,false) or use the binomial distribution formula to calculate each of the probabilities P(R = i). P(R-i) 3. 4. (d) Calculate the expected value, variance and standard deviation of R, using the given formulas for the expected value, variance and standard deviation of a binomial random variable, in terms of n, p, and e (whereq=1-p). expected value: E\R] = np= variance: Var(R) = npg = standard deviation: SD(R) = Vmpg=

Answer 1

Please upvote my answer if you like it

3 7 red marbles and 3 blue marbles as possible values of R: 0, 1, 2, 3, 4,5 " " " B! 0,1,2,3 a "R+B: 5 by for a random voniable to be binomial, s Every trial an chaw should be independent i) two possible outcomes: Succus and Palere ens p (Surcers) =P (which is constant) Here, as the chawn are with replacement, so the probability of getting selected from one trial to another remain constant. 1. Also, the outcomes nee are independent There are finite no. of Inials . Therefore, R is a binomial random voniable with n=5 and p = 0.7 (as 7 to red balls out of 10 balls in Kokal) ey PCR=) - 5CM (0.4)(0.375-* Then, il P(R=;) 0.00243 802835 PWN-O 0.1323 0.3087 0.36015 0-16807 dy E(R) = np = 3.5 VCR) = np q = 1,05 , SDCR) = V105 - 1.0247