Find the conditional expectation of (a) Y given X (b) X given Y.
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- Derive the value of k that minimizes the variable. expectation E[(X-k)²], where X is a randomFormula: Expected value = E(x) = x1P1+x2P2+ ... + xnPn Where x = the outcome and P = probability of outcome Dr. Kimball likes to go fishing with his son. To motivate his son, he pays him for the first fish that he catches. There are two types of edible fish that his son can catch: Trout and Salmon. If he catches a Trout he pays him $5, if he catches Salmon $3. There is a 20% chance that he will catch a trout and 50% that he will catch a Salmon. On average, how much does Dr. Kimball pay his son on a trip?For a recent evening at a small, old-fashioned movie theater, 30% of the moviegoers were female and 70% were male. There were two movies playing that evening. One was a romantic comedy, and the other was a World War II film. As might be expected, among the females the romantic comedy was more popular than the war film: 85% of the females attended the romantic comedy. Among the male moviegoers the romantic comedy also was more popular: 65% of the males attended the romantic comedy. No moviegoer attended both movies. Let F denote the event that a randomly chosen moviegoer (at the small theater that evening) was female and F denote the event that a randomly chosen moviegoer was male. Let r denote the event that a randomly chosen moviegoer attended the romantic comedy and R denote the event that a randomly chosen moviegoer attended the war film. Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses.
- Solve the below problem. Table 1 contains the probabilities associated with each possible pair of values for Y, and Y, and is known as the joint probability function for Y,and Y2 Table: Probability function for Y, and Y, Yı_ y2 0 1 2 0 1/9 2/9 1/9 2/9 2/9 0 1 | 2 1/9 0 Find F (1, –2) and F(3,3).Probabilities have all the the following properties EXCEPT Ο0 < Σ P(x) <1 0 ΟΣ P(x) Ο0 < P(x) <1 1 - P( NOT A) = P(A) = 1The probability function of the amount of soft drink in a can is f(x)=4cx for11.5 <X< 12.5 oz. Determine the value of c such that f(x) represents a p.d.f..Then, find the following probabilities:(a) P(X > 11.5), (b) P(X < 12.25), and (c) P(11.75 <X< 12.25).
- Sarah and Thomas are going bowling. The probability that Sarah scores more than 175 is 0.5 , and the probability that Thomas scores more than 175 is 0.1 . Their scores are independent. Round your answers to four decimal places, if necessary. (a) Find the probability that both score more than 175 . (b) Given that Thomas scores more than 175 , the probability that Sarah scores higher than Thomas is 0.4 . Find the probability that Thomas scores more than 175 and Sarah scores higher than Thomas.J and K are independent events. P(J|K) = 0.6. Find P(J).Which of the following statements are true 1. That the expected value operator E(X) is positive means that E(X)2 0 for all X 2. The expected value operator fulfills E(aX+bY+c)=aE(X)+bE(Y)+c 3. The conditional expected value E(X|Y) is the function h(X) of X that minimize the expected absolute error E(|h(X)-Y|) 4. If X and Y are independent variables so applies to the moment generating function for the sum X+Y that ox+y(s) = ¢x(s)· Þy(s)
- Let X1, X2, . . . are independent indicator variables with different probabilities of success. That is, P(Xi = 1) = pi. Define Yn = X1 + X2 + . . . + Xn. Find E(Yn), V ar(Yn) and coefficient of variation of YnPossible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities 0.35, 0.15, 0.35, and 0.15, respectively. (a) Calculate E(X) and then E(5 - X). E(X) E(5-X) = (b) Would the repair facility be better off charging a flat fee of $70 or else the amount $ 150 (5-X) The repair facility ---Select--- be better off charging a flat fee of $70 because E ]= 150 (5-X)] ? Note: It is not generally true that : E ( =) = E(Y)The circuit shown below operates if and only if there is some path of functional devices from left to right. The probability that each device functions is shown for each device and the devices operate independently of each other. What is the probability that the circuit operates? 0.9 0.9 0.8 0.95 0.95 0.9 (A) None of these (B) 0.5263 (C) 0.1642 (D) 0.9850 (E) 0.9702
