a) What is the probability that X > -5? b) What is the expected value of T? c) What is the variance of T?[

Let X - binomial (n, p) and Y ~ binomial (m, p) be independent. a. Derive the MGF of W = X+Y. b. By the uniqueness property of the MGF, what is the probability distribution of W? c. Find the mean and variance of W using its MGF.

Let X be a discrete random variable that takes values -1, 0, and 1 with probabilities 0.2, 0.5, and 0.3, respectively. What is the variance of X?

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Q1 The travel time (T) from district A to district B in a city may be 0.5, 1.0, 1.5, 2.0, 2.5 or 3. and the corresponding probability mass function is given as shown in the figure below. a) Find the mean value of the travel time. b) Find the modal value. c) Find the variance, standard deviation and coefficient of variation of the travel time. d) What is the probability that the travel time will be less than or equal to 1.5 hour P(T <1.5) =? 0.35 0.30 0.3 0.25 0.25 0.20 0.2 ' 0.15 0.10 0.10 0.1 0.05 0.05 0.5 1 1.5 2 2.5 3 I (hours) (1)'d

Q10. Z-score If Z is standard normal variable use the table of standard normal probabilities to find and draw the diagram. a) P(z2.13)

3. Find a z value such that the probability of obtaining a larger z value is only 0.15.

32 - The random variable X, which shows the grades of the students in a class in the exam of the statistics course, has a normal distribution with a mean of 80 and a variance of 25. Which of the following is the lowest grade with a probability of 0.3015?    a) 32.5  B) 55  NS) 82.5  D) 68  TO) 89

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Solve for (D)