# Work these problems on a separate sheet of paper. Staple sheets together, in order. Be neat. Always giveenough work and clear explanation so that fellow students could follow what you did (fromstart to finish) just by reading your paper.1. (See. 3.3) A certain brand of tuperware is available in four different capacities: 8em2, 16cm2, 2temand 30cm. Let X = the capacity of a piece of tuperware of this brand sold at a certain store. Supposethat X has pmf16 2430P{x) | .1 | .4 | 23(a) Compute E(X), E(x?) and V(X).(b) If the price of a piece of tuperware having capacity X is given by 60X-545, what is the expeetedprice paid by the next customer to buy a piece of tuperware?(e) What is the variance of the price paid by the next customer?(d) Suppose that although the capacity of apiece of tuperware is X, the actual capacity is given byX-009X. What is the expected actual capacity of the piece of tuperware purchased by thenext customer?2. (Sec. 3.3) Possible values of X, the number of calculators from a public high school classroom submittedfor repair that must be replaced, are 1, 3, 5 and 7. with corresponding probahilities .10,.25, 35 and30, respectively(a) Calculate E(X) and E(s- X)(b) Would the repair facility make a larger profit if they charged a flat rate of S90 regardless of thenumber of components needing repair, or if they charged the amount \$185/(8-X)?3. (Sec. 3.3) A Bernoulli random variable X is one which can only take the values 0 or 1. SupposeP(X 1)-p, ie. the probability of "success" is p(a) Find E(X) in terms of p.(b) Find E(X) in terms of p.(e) Verify that V(X) = p(1 -- p).4. (Sec. 3.4) In 2016, the United States Census Bureau estimates that 1 in 13 children in the UnitedStates have a food allergy of some sort. Consider selecting a random sample of 30 children and let Xbe the number in the sample who have a food allergy. Note that X has a binomial distribution.(a) Determine both P(X < 3) and P(X < 3)(b) Determine P(X 4).(e) Determine P(1X< 4.(d) What is the expected value of X7 What is the standard deviation of X?(e) In a class consisting of 45 children, what is the probability that none of them have a food allergy?Cs Scanned withCamScanner

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If the price of a piece of tuperware having capacity X is given by 60X-545, what is the expected price paid by the next customer to buy a piece of tuperware? help_outlineImage TranscriptioncloseWork these problems on a separate sheet of paper. Staple sheets together, in order. Be neat. Always give enough work and clear explanation so that fellow students could follow what you did (from start to finish) just by reading your paper. 1. (See. 3.3) A certain brand of tuperware is available in four different capacities: 8em2, 16cm2, 2tem and 30cm. Let X = the capacity of a piece of tuperware of this brand sold at a certain store. Suppose that X has pmf 16 24 30 P{x) | .1 | .4 | 2 3 (a) Compute E(X), E(x?) and V(X). (b) If the price of a piece of tuperware having capacity X is given by 60X-545, what is the expeeted price paid by the next customer to buy a piece of tuperware? (e) What is the variance of the price paid by the next customer? (d) Suppose that although the capacity of apiece of tuperware is X, the actual capacity is given by X-009X. What is the expected actual capacity of the piece of tuperware purchased by the next customer? 2. (Sec. 3.3) Possible values of X, the number of calculators from a public high school classroom submitted for repair that must be replaced, are 1, 3, 5 and 7. with corresponding probahilities .10,.25, 35 and 30, respectively (a) Calculate E(X) and E(s- X) (b) Would the repair facility make a larger profit if they charged a flat rate of S90 regardless of the number of components needing repair, or if they charged the amount \$185/(8-X)? 3. (Sec. 3.3) A Bernoulli random variable X is one which can only take the values 0 or 1. Suppose P(X 1)-p, ie. the probability of "success" is p (a) Find E(X) in terms of p. (b) Find E(X) in terms of p. (e) Verify that V(X) = p(1 -- p). 4. (Sec. 3.4) In 2016, the United States Census Bureau estimates that 1 in 13 children in the United States have a food allergy of some sort. Consider selecting a random sample of 30 children and let X be the number in the sample who have a food allergy. Note that X has a binomial distribution. (a) Determine both P(X < 3) and P(X < 3) (b) Determine P(X 4). (e) Determine P(1X< 4. (d) What is the expected value of X7 What is the standard deviation of X? (e) In a class consisting of 45 children, what is the probability that none of them have a food allergy? Cs Scanned with CamScanner fullscreen
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