Locate the mean (x), mode Xp and median Xm for the probability density P(x) and F(x) shown below
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Assume that the battery life in both cases follows an exponential distribution. a. Show the probability density function for battery life for the Droid Razr Maxx phone when its primary use is talk time. b. What is the probability that the battery charge for a randomly selected Droid Razr maxx phone will last no more than 15 hours when its primary use is talk time? c. What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last more than 20 hours when its primary use is talk time? d. What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last no more than 5 hours when its primary use is Internet Applications?C1. Let X be a continuous random variable with PDF f(x) = (2-x) ² for -1 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X.The random variable X has the probability density function 2x, 0Delta Airlines quotes a flight time of 2 hours, 3 minutes for a particular flight. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 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: 114, 120, 126, 132. 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 120 on the horizontal axis. A 1/12 unit long vertical line segment begins at 126 on the horizontal axis. A 6 unit long horizontal line segment begins at the tickmark labeled 120 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 area. The…Find the mean and variance of the uniform probability distribution given by f(x)=1/n for x=1,2,3,4……Help me for thisProb. 4 (Gaussian Distribution) Consider a standard Gaussian random variable with probability density function given by 1 fx(x) = еxp V2n - c0The table gives the joint probability distribution of the number of sports an individual plays (X) and the number of times she may get injured while playing (Y) X=1 X=2 X=3 0.12 0.08 0.15 0.06 0.05 0.05 0.10 0.03 0.15 0.15 0.04 0.02 Y=4 Y=3 Y=2 Y=1 The covariance between X and Y, oxy, is (Round your answer to two decimal places Enter a minus sign if your answer is negative) The correlation between X and Y, corr(X, Y), is (Round your answer to two decimal places Enter a minus sign if your answer is negative.) 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