Ifp and q are independent variates uniformly distributed over the interval (-1, 1), find the probability that the equation x² + 2px + q = 0, has real roots.
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- Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.If Var(X1) = 2, Var(X2) = 4, Var(X3) = 3, Cov(X1, X2) = 1, Cov(X1, X3) = -2, and X2 and X3 are independent, find the mean and variance of Y = X1 – 2X2+3X3.If 25% of the oranges produced by a farm is defective in a random sample of 20 oranges, then if the variable X represents the number of defective oranges in the required sample: Calculate (X> 3) exactly
- E and F are independent variables with variances of 7 and 9, respectively. Given this, Var(2E - F + 2) = ? Show complete solution.Suppose, you are given a straight-line equation, 3x+2y=6 where x and y both of them are integer numbers and ∣y∣<12. Compute the probability when ∣x∣=∣y∣.In a fish restaurant, population variance for fish to go bad is at least 4 days. After buying a new cooling system, its expected to be less than 4 days. After buying the new cooling system, 10 fish are tested and with an average of 8 days without going bad with a population variance of 3 days. Test with 95 confidince if the population variance is really less than 4 days. (use chi square test for the lower-side by using the formula and not the excel please)
- Find the maximum likelihood estimator by getting the derivative and equating it to 0The number of clients a store has during a week is Poisson distributed with - 25. The amount of money spent by each client follows a random = el,000t+250t2. Assuming the mean A variable with moment generating function o(t) independence between the number of clients, and the amount of money spent by each client. Find the mean and variance of the amount of money received by the store every week.The life X (in years) of a voltage regulator of a car has the pdf: X 3 - (-/-)². 3x2 73 0≤x≤∞ What is the probability that this regulator will last at least 7 years? Give your answer to 3 decimal places and show working.