Please show and explain the steps! Solve only (d) and (e)! There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights at which the commuter must stop on his way to work, and X, be the number of lights at which he must stop when returning from work. Suppose that these two variablesare independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n = 2).X112P(x,) | 0.4 0.2 0.4u = 1, o2 = 0.8(a) Determine the pmf of T, = X, + X2.to134P(t,)(b) Calculate uTHow does it relate to u, the population mean?2(c) CalculateHow does it relate to o?, the population variance?2g2(d) Let X, and X, be the number of lights at which a stop is required when driving to and from work on a second day assumed independent of the first day. Wwith T, = the sum of all four X,'s, what now are the values of E(T) and V(T,)?E(T,) =V(T.) =(e) Referring back to (d), what are the values of P(T, = 8) and P(T, 2 7) [Hint: Don't even think of listing all possible outcomes!]P(T, = 8) =P(T, 2 7) =

(d). Find the values of E(T0) and V(T0): The values of E(T0) and V(T0) are obtained as given below:

which the commuter must stop on his way to work, and X, be the number of lights at which he must stop when returning from work. Suppose that these There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights are independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n = 2). 1 2 P(x,) 0.4 0.2 0.4 H = 1, o = 0.8 (a) Determine the pmf of T, = X, + X2- 1 3 4.

which the commuter must stop on his way to work, and X, be the number of lights at which he must stop when returning from work. Suppose that these There are two traffic lights on a commuter's route to and from work. Let X, be the number of lights are independent, each with the pmf given in the accompanying table (so X,, X, is a random sample of size n = 2). 1 2 P(x,) 0.4 0.2 0.4 H = 1, o = 0.8 (a) Determine the pmf of T, = X, + X2- 1 3 4.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

See similar textbooks

Similar questions

There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 p(x1) 0.1 0.2 0.7 ? = 1.6, ?2 = 0.44 (a) Determine the pmf of To = X1 + X2. to 0 1 2 3 4 p(to) (b) Calculate ?To. ?To = How does it relate to ?, the population mean? ?To = · ? (c) Calculate ?To2. ?To2 = How does it relate to ?2, the population variance? ?To2 = · ?2
There are two traffic lights on a commuter's route to and from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). Can you help me with 3 and 4?
There are two traffic lights on a commuter's route to from work. Let X1 be the number of lights at which the commuter must stop on his way to work, and X2 be the number of lights at which he must stop when returning from work. Suppose these two variables are independent each with pmf given in the accompanying table (so X1, X2 is a random sample of size n = 2). x1 0 1 2 p(x1) 0.2 0.5 0.3 μ=1.1,σ=0.49 a. Determine the pmf of T0=X1+X2
If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y =X1 + 2X2 + X3 is not a sufficient estimator of θ. (Hint:Consider special values of X1, X2, and X3.)
Let X and Y be two random variables with E (X) = 1, E (Y) = 2, Var (X) = 1, Var (Y) = 2, !! Cov (X, Y) = 0.5. For what values of a and b such that the random variable aX + bY have mean 3 and variance 4 ?
Let X1 and X2 be independent chi-squared random variables with r1 and r2 degrees of freedom, respectively. Show that, (a) U = X1/(X1+X2) has a beta distribution with alpha = r1/2 and beta = r2/2. (b) V = X2/(X1+X2) has a beta distribution with alpha = r2/2 and beta = r1/2
Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).
If X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2,find P{X1 < X2} and P{X2 < X1}.
Let X1, …, Xn be a random sample from a N(0, σ²) population. Find the MLE of σ.
Let p1 and p2 be the respective proportions of women with iron-deficiency anemia in each of two developing countries. A random sample of 1900 women from the first country yielded 513 women with iron-deficiency anemia, and an independently chosen, random sample of 1700 women from the second country yielded 515 women with iron-deficiency anemia. Can we conclude, at the 0.10 level of significance, that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country? Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. a. State the null hypothesis H0 and the alternative hypothesis H1. b. Find the values of the test statistic. c. FInd the p-value. d. Can we conclude that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country?
Let X1, X2, X3,....., Xn be the independent identically distributed random variables and let Sm = X1 + X2 + .... + Xm. Assume that P(Sn = 0) = 0 and if m ≤ n then E(Sm/Sn) equals
If X is Poisson random variable with parameter λ, compute E[1/(X + 1)]