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- (b) Define the Integral of a non-negative random variable and state the associated well-known theorem.Let P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).The amount of time a cashier spends cashing out each customer at a store is modeled by an exponential random variable with parameter λ =1/3 minutes. Assume that the time the cashier spends with each customer is independent and identically distributed. Approximate the probability that the cashier will spend more than sixty minutes cashing out a total of eighteen customers. You may leave your solution as a real number rounded to fourdecimal places or you may leave your solution in terms of the standard normal CDF, Φ.
- X is a discrete random variable such that the possible values are {a, a+1, a+2, ... b-1, b}. The random variable has a mean of 7 and a variance of 4. What is the Pr(X<=6|X>4)?Let X be a strictly positive random variable. Determine which of the following quantitiesare larger:(a) E(X^4) or (E(X))^4(b) E(X^1/9) or (E(X))^1/9(c) E(X^3 + 4X^2 + 9) or (E(X))^3 + 4(E(X))^2 + 9(d) E(e^X ) or e^E(X)(e) E(arctan(X)) or arctan(E(X))Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2 otherwise. Submit your answer in fractional form.
- For each characteristic, decide whether the random variable is continuous or discrete. (a) The number of left-handed individuals in a sample of 250 people. O continuous O discrete (b) Time taken to complete an exam for students in a class. O continuous O discrete (c) Vehicle speeds at a highway location. O continuous O discrete (d) The number of accidents reported last year at a highway location. O continuous O discreteThe weekly demand for propane gas (in 100's of gallons) from a particular facility is a random variable X with pdf: f(x) = 2(1) for 1 ≤ x ≤ 2 Please find out the mean of X. 3/2-In(2) 3-2 In(2) 1/2-In(4) 3-In(2)are iid random variables having mean u and variance o?. Form the random Suppose f1, 2, . sum SN .. E1 +..+ EN. (a) Derive the mean and variance of SN when N has a Poisson distribution with parameter d. (b) Determine the mean and variance of SN where N has a geometric distributions with mean (c) Compare the behaviors in (a) and (b) as A→ o.
- Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, the mean of the distribution is 4.8. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient’s doctor are 4.2, 4.9, 4.5, 4.1, 4.4, 4.3 with a sample mean of (x̄= 4.4) and a sample standard distribution s =.28. Do the given data indicate that the mean RBC count for this patient is lower than 4.8? Use α = 0.05. f)Based on your calculation the P-Value falls between what range?__________ < P -Value < ____________ g)Is the P-Value range greater than or less than the level of significance (α)? h)Do you reject or fail to reject the null hypothesis? i)Is there sufficient or insufficient evidence to support the claim that the average RBC count for this patient is less than 4.8?Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, the mean of the distribution is 4.8. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient’s doctor are 4.2, 4.9, 4.5, 4.1, 4.4, 4.3 with a sample mean of (x̄= 4.4) and a sample standard distribution s =.45. Do the given data indicate that the mean RBC count for this patient is lower than 4.8? Use α= 0.10. a)What is the null hypothesis? H0= _________ b)What is the alternate hypothesis? H1__________ c)Calculate the degrees of freedom.___________ d)What test willbe used in this example? e)Calculate the test statistics (t). f)Based on your calculation the P-Value falls between what range? < P -Value < g)Is the P-Value range greater than or less than the level of…Let x be a random variable that represents red blood cell (RBC) count in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, the mean of the distribution is 4.8. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient’s doctor are 4.2, 4.9, 4.5, 4.1, 4.4, 4.3 with a sample mean of (x̄= 4.4) and a sample standard distribution s =.28. Do the given data indicate that the mean RBC count for this patient is lower than 4.8? Use α = 0.05. a)What is the null hypothesis? H0= _________ b)What is the alternate hypothesis? H1__________ c)Calculate the degrees of freedom___________ d)What test will be used in this example? ________________________________ e)Calculate the test statistics (t)
