(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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- box A and box B both contain the numbers 1 2 3 and 4. Construct the probability mass function and draw the histrogram of the sum when one number from each box is taken at a time, with replacement.The probability density function for the life span of an electronics part is ft)- 0.06e-0.06, where it is the number of months in service. (Round your answers to three decimal places.) (a) Find the probability that a randomly selected part of this type lasts longer than 48 months. (b) Find the probability that a randomly selected part of this type lasts longer than 48 months given that it lasts longer than 36 months.An electronic scale at an automated filling operation stops the manufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.02 and fills are independent. Determine the probability mass function of the number of fills (x) before the manufacturing line is stopped.
- Study the probability mass function below and find the probability: 1.) P(X ≥ 4) 2.) P(X < 2) 3.) P(X ≤ 2)In 1938, a physicist named Frank Benford discovered that the number 1 appears in the first digit of random data more often than the number 2, the number 2 more often than the number 3 and so on. In general, the probability of occurrence of the first digit of a number can be written in the form of a probability function x + 1 P(X = x) = log. X a. Prove it P(X = x) = log ) untuk x = 1,2,3,4...,9 x+1 X x = 1,2,3,4..., 9 is a probability mass function 2 b. Find the cumulative distribution function of X!Let the Probability Mass Function as follows: f(-1)=0.2, f(2)=0.3, f(3)=0.35 and f(0)=??, Then F(2)- a 0.35 O b.0.65 c0.15 d. 0.3 ge
- Let X equal the IQ of a randomly selected American. Assume X ~ N( μ μ {"version":"1.1","math":"μ"} =100, σ σ {"version":"1.1","math":"σ"} =4). What is the probability that a randomly selected American has an IQ below 90?A company uses wood chips in the manufacture of processed wood pieces of various sizes. Suppose the tons of wood chips T used per day has a probability density function f(T) = 0.25e-0.25T (a) Find the probability of using more than 4 tons of wood chips in a day. (Round your answer to three decimal places.) (b) Find the number of tons 7 (to the nearest ton) so that the probability of using more than 7 tons in a day is 0.07. tonsIf 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 0.45
- 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, ..., 1000Suppose that the probability density function of a random variable X is as follows: f(x)= cx, for0<x<4; 0, otherwise. (a) Find c.(b) Find the cumulative distribution function F and sketch it.Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.33 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) 0 1 2 3 4 5 6 7 8 P(X=x) 0 1 2 3 4 5 6 7 0.1350 0.1330 0.2322 0.1965 0.2633 ✓ ✔ (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) 0.1350 0.268 0.5002 0.6967 x