Question

SCAN will be alive at Je of the three we of age 20 is ali sare indepen access probat Chapter 53 - Mean (Expected Value) and Stord Deviation of Probability is BUS210 Name: Date Class Time: MWE The Weighted Mennor Expected Value of random variable X is EX) > 16) un in Table presents the not because th e to determ "I by part The Variance, and Standard Deviation, a of Xare 0? = VAR(X) = (x-2) (0 O SD (X) + VAR(X) 1. Calculate the expected value of the number of heads after tossing a coin 3 times licatio: me. Fos .14. the 1. 2. In bidding for a remodeling project, a carpenter determines that he will have a net profit of $5,000 be gets the contract and a net loss of $100 if his bid fails. If the probability of his getting the contract is calculate his (a) Expected return, E(X) and (b) Standard Deviation, * (*) (x - H) (x-4² | (x,-4² f(xD) $5,000 0.2 -$100 Total 4900 (a) E(X) = u = (b) SD(X) = 0 =

Answer 1

1x. fox;) x;fcx;) (x;-) (x,-1) (x,-4} fox) 5000 0.2 1000 4080 16 646400 3329280 - 100 0.8 -80 83 2320 920 3060 1768 6800 14161600 a) Elx) = M - Ex;fcx, ) - 1000 +(-80) = 920 -1020 LOLO400 bor - E (x; -Mf f(x) = 4161600 6=562 = 2040 SD(x) = 6 - 2040 Let the success event be the applicant hired at the new data center. For then success probability , p = 40% - 40 -0.4 Given that n=5. . Let & be the number of applicants hired. Then x ~ Binomial (5, 0.4) a) P (two applicants are hired) = P(x=2) = 54 (0.47² (1-0.4) 5-2 = 10 (0.4² (0.6% - 0.3456

6) Plat least one applicant is hired) = P(x>01) = 1- P(x-1) 1- P(x-0) = 1 - 560 (0.4) (0.6) = 1 - (0.6) 5D 0.92224 c) Platmost two applicants are hired) =P ( x + 2) = P(X=0) + PCX =1) + P(x =2) = 9 (0.4% (0.6) + 5, (0.4)(0.67 +52 (0.4² (0.6) bost04 + = 0.07776 + 0.2592 + 0.3456 = 0.68256 d) Expected number of applicants, i = E(X) = np = 5x0.4 - 2