1. P(X= 0) 2. P(X = 1) 3. P( x= 0 or Xe1) P(xs 2) P (x<2) Pe. 20 6. Thursday, April 8, 2021 8:06 n= 5 7. 8. X= 2 usual binom pdf (n,P,x) linom edf (n.P,x) X< a X> a exact X 4. P(x>3) 9. Find M, 6 5. P(x23) |- binomedf 6- Vnp(i-P)
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- The lifetime of a certain type of TV remote control is given by Y . Suppose Y has approximately exponential distribution with mean 8 years. a) Find the probability that a remote control of this type will last more than 15 years. b) Find the probability that of eight such remote controls at least one will last more than 15 years. c) What should the warranty period for these remote controls be if the manufacturer wants 85% of the remote controls to last beyond the warranty period? d) What is the moment generating function of Y .where is the graphical estimation method (by hand)X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2
- right tailed t-test; df: 10, alpha: 0.05Q9: Assume that a researcher wants to estimate the proportion of “A” grade scorers in STAT101 course for the population of SEU students in 2020. Assume also that the proportion of “A” grade scorers in 2020 is not known. How many SEU students must be surveyed from STAT101 course in order to be 90% confident and the margin of error should not exceed two percentage points? (Given zα/2 = 1.64). 1- 1821 2- 1781 3- 1618 4- 1681If X is exponentially distributed with parameter λ and Y is uniformly distributed on the interval [a, b], what is the moment generating function of X + 2Y ?
- A mass m moves along the x-axis subject to an attractive force given by 19mx/2 and a retarding force given by , where x is its distance from the origin and is a constant. A driving force given by , where A is a constant, is applied to the particle along the x-axis. Write down the equation of motion. What value of results in steady-state oscillations about the origin with maximum amplitude? What is the maximum amplitude? what is the Q value?Please do not give solution in image format thanku 1.Suppose that the moment generating function of a random variable X is MX(t)=exp(2e^t−2) and that of a random variable Y is MY(t)=((4/5)e^t+1/5)^16. If X and Y are independent, find each of the following. (a) P{X+Y=2}= (b) P{XY=0}= (c) E[XY]= (d) E[(X+Y)^2]= ———A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. The pdf is f(x) = kx^2 if 0 <= x <= 2, and 0 otherwise. (a) Find the value of k. (Enter your answer to three decimal places.) (b) What is the probability that the lecture ends within 1 min of the end of the hour? (Enter your answer to three decimal places.) (c) What is the probability that the lecture continues beyond the hour for between 30 and 90 sec? (Round your answer to four decimal places.)