A projectile is blue at a target. The distance from the point of impact to the...
(1 point) The following density function describes a random variable X F(x) = m if 0 and if 8<x< 16. Draw a graph of the density function and then use it to find the probabilities below A. Find the probability that X lies between 1 and 6. Probability B. Find the probability that X lies between 5 and 10. Probability C. Find the probability that X is less than 9. Probability D. Find the probability that X is greater than...
1. A point P is chosen with a uniform probability distribution around a circle of radius r Let Z be a random variable that measures the absolute value of the distance of P from the y-axis (a) What is the mean and the variance of Z? (Hint, define an appropriately normalized uniform probability density function for the angle 0 describing the polar angle of the position P on the circle.) (b) Does your answer for the mean make sense? (c)...
Suppose that a continuous
random variable takes on the interval from 0 to 4 that the graph of
its probability density is given the blue line of Figure 7.19
on values on the interval fr t 7.2 Suppose that a continuous random variable takes on values 0 to 4 and that the graph of its probability density is given by the blue tr to e line Figure 7.19. (a) Verify that the total area under the curve is equal to...
8. A projectile is fired from the origin in a straight line towards a rectangular target and hits it perpendicularly 2 seconds later. The vertices of the rectangle are (50,100,275), (100, 0, 275), (200,50, 150), and (150, 150, 150), where units are in meters. (a) At what point did the projectile hit the rectangle? (b) The projectile was trying to hit the center of the target. How accurate was it? (c) Assuming the projectile was moving at a constant speed,...
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The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density function given by f(x)- 0, elsewhere Find (a) The value of a that makes f(x a probability density function. (b) The probability that this individual will talk (i) between 8 and 12 minutes, (i) less than...
(1 point) Scale the functions to convert them into probability density functions. Then find the expected value of a random variable with those densities. If not possible, type dne. (a) f(x) = Te-7* 0 >0, otherwise multiplier to convert f(x) into a probability density function: expected value of a random variable with this density: (b) f(x) 9 sin(2) 0< x <, otherwise 0 multiplier to convert f(x) into a probability density function: expected value of a random variable with this...
2.5.12. The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density function given by 0, elsewhere. Find (a) The value of a that makes fx) a probability density function. (b) The probability that this individual will talk (i) between 8 and 12 min, (ii) less than 8 min,i) more...
1 2 A projectile PA is launched from point A towards the east with an initial launch velocity ves and an initial launch angle of 8aA. The impact point of the projectile Pa is a point B in a valley with an ordinate, you, located below the elevation of point A. The launch from point A is instantaneously detected at point B, and a counter projectile Pa ts launched simultaneously towards the west to intercept the incoming projectile PA. Projectile...
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
Question 3 (10 point) The error in the length of a part (absolute value of the difference between the actual length and the target length), in mm, is a random variable with probability density function 0 otherwise a. Find the cumulative distribution function of the error b. What is the probability that the error is less than 0.2 mm? c. Find the mean error d. Find the variance of the error. e. The specification for the error is 0 to...