A continuous random variable X is defined to have a uniform probability density function given as follows: f(x) = }b - --a for 1.0 sx < 1.5 elsewhere Show the PDF graph of this f(x). Question ?
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- QUESTION 2 Delta Airlines quotes a flight time of 4 hours, 3 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 4 hours and 4 hours, 12 minutes. (a) Show the graph of the probability density function for flight time. The graph has a shaded area. The horizontal axis is labeled: x with the title: Flight Time in Minutes and has tickmarks labeled: 234, 240, 246, 252. The vertical axis is labeled: f(x), and has tickmarks labeled: 1/12, 1/6, 1/4. The shaded area is the region bounded by the horizontal axis and the following line segments. A 1/12 unit long vertical line segment begins at 240 on the horizontal axis. A 1/12 unit long vertical line segment begins at 252 on the horizontal axis. A 12 unit long horizontal line segment begins at the tickmark labeled 240 on the horizontal axis and the tickmark labeled 1/12 on the vertical axis. This line segment connects the two vertical line segments. The graph has a shaded…Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?Suppose there is a random variable X whose probability density function has the form (shown in image). a) Find P(X>-0.2) b) Find the 90th percentile
- If the moment generating function of a random variable Y is Find the probability density function of Y.QUESTION 10 Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X > 4) = 1/2. What are the values for a and b? a. 2 and 6 b. Cannot answer with the information given. c. 0 and 4 d. Can be any range of x values whose length (b − a) equals 4. QUESTION 11 The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a ≤ x ≤ b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices. QUESTION 12 Which of the following is true about f(x) when X has a uniform distribution over the interval [a, b]? a. The values of f(x) are different for various values of the random variable X. b. f(x) equals one for each possible value of X. c. f(x) equals one divided by the length of the interval from a to b.…Question 1) Suppose the travel time from White Plains Transit Center to SUNY WCC on public transit (Bus Route #15) follows a Uniform Distribution with a minimum time of 10 minutes and maximum time of 25 minutes. Let the random variable x represent the time from White Plains Transit Center to SUNY WCC on public transit. What is the probability Density Function, pdf, for the random variable x? Sketch the Density Curve for the random variable x. What is the probability the travel time is between 15 and 20 minutes? What is the probability the travel time is between 10 and 13 minutes?
- If X and Y are random variables and X is a geometric random variable where p = 0.1 then what is the probability mass function of Y = sin(X*pi) ?If X is an exponential random variables with rate 1, then its distribution function is given by F(x) = 1 − e−x Show that x = − ln(1 − u).Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.
- Suppose that the random variable B has the standard normal density. What is the conditional probability density function of the sum of the two roots of the quadratic equation x2 + 2Bx + 1 = 0 given that the two roots are real? KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTIONThe random variable x is known to be uniformly distributed between 1.0 and 1.5.a. Show the graph of the probability density function2.1) Suppose a random variable X has a probability density function in the attached image. a) Find the value of k that makes this a probability density function. b) Find the expected value of X.