Let X be the number of flaws on the surface of a randomly selected boiler of...
(5) 2. Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose that the distribution of X is as follows: T 1 2 3 p(x) 3 .2 .5 A a random sample of size n-3 is selected. a) find pmf of Xn and construct a histogram, b) give two smallest values of S2, (S2 is the sample variance) and find their probabilities. (5) 2. Let X be the number of...
Let x be the number of tree seedlings in a randomly selected one square meter plot in a forest. Suppose that x has a Poisson distribution with λ = 5, which corresponds to an average of five seedlings per square meter. Find the probability that a randomly selected one square meter plot contains no seedlings.
The number of flaws x on an electroplated automobile grill is known to have the following probability mass function: p(0) = 0.6; p(1) = 0.2; p(2) = 0.1; p(3) = 0.1 a) Is this random variable continuous or discrete? Justify your answer. b) Verify that this is a proper mass function c) What is the probability that a randomly selected grill has fewer than 2 flaws? Calculate the probability, and use proper probability notation. d) What is the probability that...
Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows. x 1 P(x) 0.2 2 0.4 3 4 0.3 0.1 (a) Consider a random sample of size n = 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X. 1.5 35 (b) Refer to part (a) and calculate PX $ 2.5). (c) Again...
Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows. 1 0.3 2 0.4 3 0.1 4 0.2 p(x) (a) Consider a random sample of size n = 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X. 1 1.5 2 2.5 3 3.5 4 POCO (b) Refer to part (a) and calculate...
Let X be the number of packages being mailed by a randomly selected customer at a certain shipping facility. Suppose the distribution of X is as follows. * 1 p(x) 0.2 2 0.4 3 4 0.3 0.1 (a) Consider a random sample of size n 2 (two customers), and let X be the sample mean number of packages shipped. Obtain the probability distribution of X 1 1. 5 2 3.5 PC) 04 125 x 16 X (b) Refer to part...
Let the random variable X count the number of adults out of five randomly selected adults who reported sleepwalking. The table gives the probability distribution of X X P(X=x) 0 0.142 1 0.353 2 3 0.137 4 0.042 5 0.006 A) Determine the missing probability that ensures the tables is a valid discrete probability distribution B) Compute the probability that among five randomly selected adults fewer than three report sleepwalking C) Compute the probability that among five randomly selected adults...
Let x denoted the number of flaws along a 100 m reel of magnetic tape (values of x are whole numbers). Suppose x has approximately a normal distribution with u=25 and 0=5. a. What proportion of reels will have between 20 and 40 flaws, inclusive? (Ans:0.8633) b. What proportion of reels will have at most 30 flaws? Fewer than 30 flaws? (Ans:0.8643, 0.8159)
Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table shown below: x 1 2 3 4 5 6 7 p(x) .03 .05 .09 .26 .39 .14 .04 (a) What is P(x = 4)? P(x = 4) = (b) What is P(x ≤ 4)? P(x ≤ 4) = (c) What is the probability that the selected student is taking at most five...
Let Ņ, X1. X2, . . . random variables over a probability space It is assumed that N takes nonnegative inteqer values. Let Zmax [X1, -. .XN! and W-min\X1,... ,XN Find the distribution function of Z and W, if it suppose N, X1, X2, are independent random variables and X,, have the same distribution function, F, and a) N-1 is a geometric random variable with parameter p (P(N-k), (k 1,2,.)) b) V - 1 is a Poisson random variable with...