(a) Write down the probability mass function of X. (b) Find the probability of observing an even number of tails before the first head (0 is counted as even).
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- Show that the attached image is a valid probability mass function:The time (in years) until the first critical-part failure for a certain car is exponentially distributed with a mean of 3.4 years. Find the probability that the time until the first critical-part failure is 5 years or more.A) 0.770210 B) 0.493383 C) 0.229790 D) 0.506617TF.12 The joint pdf of the lifetimes X and Y in years of two batteries working in parallel is (see picture) a) Find the probability P(Y ≤ 0.5). b) Find the expected values E(X) and E(XY).
- For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. f(x) = 195x, (0,5] 2, [0,5] 125 a) Find the mean. (Round to three decimal places as needed.) b) Find the standard deviation. O = (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)Find the value of k for the probability mass function 4 f(x) = k () , ) for x = 0,1,2. %3| 4 -The time t (in minutes) spent at a driver's license renewal center is exponentially distributed with a mean of 40 minutes. (a) Find the probability density function of the random variable t. (b) Find the probability that t is within one standard deviation of the mean. (Round your answer to one decimal place.)
- If the average number of rodents in a cotton farm whose swabs are 20 dunums is 2 per dunum, calculate The probability that a given dunam contains more than 3 rodents. b, find the value of the constant C that makes the following function a probability mass function F(x) C 0.15 0.45A commuter encounters four traffic lights each day on her way to work. Let X represent the number of these that are red lights. The probability mass function of X is as follows. 0 1 2 3 4 P(X = x) 0.1 0.3 0.3 0.2 0.1 What is the probability that in a period of 100 days, the average number of red lights encountered is more than 2 per day?In a batch of 26 pedometers, 3 are believed to be defective. A quality-control engineer randomly selects 4 units to test. Let random variable X= the number of defective units that are among the 4 units tested. a. Find the probability mass function f(x) = P(X =x), and sketch its histogram. b. Find P(X= 1). What does this number represent? c. Find P(X>1). What does this number represent? ..... Using the hypergeometric probability distribution model, set up an expression that can be used to find a single ordered pair in the probability mass function f(x) = P(X= x). 3 23 tion of -X f(x) = P(X = x) = (Simplify your answers.) 26 a. Find the probability mass function f(x) = P(X= x). find f(x) = {0.59230, 0.35538, 0.05077, 0.00154} (Type an ordered pair. Use a comma to separate answers as needed. Round to five decimal places as needed.)
- A shop receives a shipment of 1000 lamps. The probability that any individual lamp is defective is 0.2%. Assume the defectiveness is independent of cach lamp. Let X be the number of defective lamps in the batch of 1000. What is the probability mass function of X? O P(X = k) = (00) 0.002* (1 – 0.002)1000 , k = 0,1, 2, ..., 1000 O P(X = k) = 0.002* (1 – 0.002)1000–&, k = 0, 1, 2, .….., 1000 O P(X = k) = (1000) 0.002* (1 – 0.002)1000 , k = 1, 2, ..., 1000 O P(X = k) = (00)0.002100- (1 – 0.002)*, k = 0, 1, 2, ..., 1000For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. 1 f(x) = x, [5,9] 28 a) Find the mean. %3D (Round to three decimal places as needed.) b) Find the standard deviation. (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)Find c to get a probability mass function.