3 Suppose Z = N (0,1) and Y= ez Find E(Y)
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- There is a chance that a bit transmitted through a digital transmission channel is received in error. Let X equal the number of bits in error in the next four bits transmitted. The possible values of X are {0,1,2,3}. Suppose that P(X=0)=0.6, P(X=1)= 0.3, P(X=2)= 0.05, P(X=3)= 0.05 What is the CDF of X at 3? i.e., what is F(3)? a). 0.6 b). 0.9 c). 0.95 d). 1 e). none of above For the random variable defined in question 12, if we know that Var(X)=0.6475, what is the standard deviation of X? a). 0.55 b). 0.6475 c). 0.419 d). 0.8 e). none of aboveIf y* = e* , then y equals A B none of the given choicesCalculate the length of are of y = 2x³/2 for 0≤x≤1
- 11. Given P(A) = 0.25, P(B) = 0.28, and P(B|A) = 0.28, are A and B independent or dependent?Assume that W (t) is a standard Brownian motion and that S(t) is a random variable defined as S(t) = 8 · 2W(t). DetermineSuppose 10% of the population of WVU students has tested positive for COVID-19, W1 represents the part of the population that has tested positive and W2 represents those who tested negative. X denotes a test result that the person has tested positive for COVID-19. P(W1) = 0.10 individual tested positiveP(W2) = 0.90 Individual tested negativeP(X|W1) = 0.80 test shows the individual tested positive and is correctP(X|W2) = 0.30 test incorrectly shows the individual is positiveRandomly select an individual and preform the test. The result shows the person tested positive, what is the probability that the test is correct? Use Bayes' theorem to solve.
- CBS news reported that 4% of adult Americans have a food allergy consider selecting 10 adult Americans at random define the variable x as: x= number of people in the sample of 10 that have a food allergy a. p(x<3) b. p(x lesss than or equal to 3) c. p (x greater than or equal to 4) d. p (1 less than or equal to x less than or equal to 3)Jerry is considering opening a new ice cream store at a certain location on State Street in Madison. Jerry conducts some analysis and determines that a given location is acceptable only if the number of pedestrians passing the potential location averages more than 100 per hour. To check if this location is acceptable, Jerry records the number of pedestrians observed for each of 40 hours. Jerry finds that the average number of pedestrians that pass the potential location during each of the 40 hours he was observing, is 105.7 per hour. Jerry assumes that he knows the population standard deviation to be 16. Can Jerry conclude at the 1% significance level that the potential location for the ice cream store is acceptable? a. What is the correct set of hypotheses? Answer: Ho: u = 100 and H1: u> 100 v b. Determine the p-value Answer: 0.0122 c. Interpret the results Answer: There is not enough evidence d. Jerry is concerned with committing a Type II error. Determine the probability of Type II…If ? (?) = ?4 – 12?2 + 7, how many critical points and inflection points are there? Select one: a. 2 critical points and 0 inflection points b. 2 critical points and 1 inflection point С. 3 critical points and 2 inflection points d. 2 critical points and 1 inflection point e. 2 critical points and 2 inflection points
- 7. Suppose A and B are independent and mutually exclusive. P(A) = 3/10. Can you determine P(B)?If X is the number of heads obtained in four tosses of a coin, the 1 is 1+X mode of Y =A bag contains 3 red balls, 2 yellow balls, 2 green balls. Suppose that you pick three balls at random (without replacement). Let R denote the number of red balls and Y the number of yellow balls. Find E(R²Y³).
