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- Derive the variance of the Student's t distribution using the definition Var (x) = ELX2] - EX)² .Let P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).Suppose that X and Y are random variables where the conditional expected value of Y given X is given by E (Y|X) = 3X + 6 If X has the expected value 0 and variance Var(X)=9 determine the minimal possible value of the variance Var(Y) of Y./
- 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)
- Which value for X will result in the greatest relative frequency give discrete random variable X,when X~B(4,1/10)?The PDF of a random variable X is given by fx(x) = 4x (9 —x²)/81, 0≤x≤3. Find the mean, variance and third moment of X. CS Scanned with CamScannerSuppose the variance of the difference of two random variables X and Y is zero. Then, show that X = Y + c for some constant c almost surely. Also find the value of c.
- If X is distributed as a normal distribution with a mean value of 10 and a variance equal to 3 and Y is distributed as a normal distribution with a mean value of 15 and a variance equal to 8, what is the probability distribution of (X-Y)?From the data set of a class, a student taking a final exam is random variable with mean equal to 50 and variance is 25. Find an upper bound for the student probability that a student's exam score will between 40 and 60.* Let X is a Gaussian random variable with zero mean an variance o. Y = X. Find mean of Random Variable Y.