4 ofthese15 ofthese3 of(a) 1.0211(c) 1.5207(e) 1.2962these2(a) 0.1111(c) 2.3333(e) 12.93752 ofthese16 tickets total3FIG. 5.2 ofthese26. Let X be the random variables described in Fig-ure 5. Find E(√x + 1).(b) 2.3125(d) 0.4613XRandom drawfrom the box27. Let X be the random variable described in Figure 5.Find E(X³ | X < 2).(b) 0.5625(d) 1.3125

Introduction: There are a total of 16 tickets in the box. The random variable X denotes the number…

Answered: 4 of these 5 of these 3 of (a) 1.0211…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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You study a population and are interested in the proportionpthat has a certain characteristic. You are unaware that this proportion of the population isp=0.67. You have taken a random sample of sizen & 129of the population and determined that the proportion of the sample having the characteristic isp=0.73. His sample is Sample 1 in the following table. (In the table, Sample 1 is indicated by "M1", Sample 2 by "M2", and so on). (to) Based on Sample 1, plot the confidence intervals of80%and of95%for the population proportion. Use1,282for the critical value for the confidence interval of80%, and use1960 for the critical value for the confidence interval of95%. (If necessary, you can refer to a list of formulas.) • Write the upper limit and the lower limit on the graphs to indicate each confidence interval. Write the answers with two decimal places. • For the points ( ♦and ◆), write the population proportion,0.67. 0.47 0.47 80% confidence interval 0.65 X 0.84 0.84 0.47 0.47 95% confidence…
Let X be a random variable defined by 2 3 P(X = x) k 2k 2k 2k 2k Then E(X) and V(X) are equal to: None of these O E(X)=13/5 and V(X)=41/25 O E(X)=20/9 and V(X)=140/81 O E(X)=27/11 and V(X)=206/121
B5. Let X₁, X₂, ..., Xn be IID random variable with common expectation µ and common variance o², and let X = (X₁ + + X₂)/n be the mean of these random variables. We will be considering the random variable S² given by (a) By writing or otherwise, show that S² (b) Hence or otherwise, show that n S² = (x₁ - x)². = Ĺ(X₂ i=1 X₁ X = (X₁-μ) - (x-μ) = Σ(X; -μ)² - n(X - μ)². i=1 ES² = (n-1)0². You may use facts about X from the notes provided you state them clearly. (You may find it helpful to recognise some expectations as definitional formulas for variances, where appropriate.) (c) At the beginning of this module, we defined the sample variance of the values x₁, x2,...,xn to be S = 1 n-1 n i=1 ((x₁ - x)². Explain one reason why we might consider it appropriate to use 1/(n-1) as the factor at the beginning of this expression, rather than simply 1/n. B6. (New) Roughly how many times should I toss a coin for there to be a 95% chance that between 49% and 510/ of my nain toon land Honda?
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sar Suppose that we also have the following. E(X)=-5 E(Y)=8 E(Z)=6 Var (X)=24 Var (Y) = 16 Var (Z) = 33 Compute the values of the expressions below. E (4Y+4)= 36 E(-4Z+2X)- -3 = 11.33 Var (4Y)-2= 254 E(-x²) = 49 0|0 X
(3) Let X be a random variable with p.d.f. 2k 3x f(x)= I
A red die is rolled and then a green die. Let X=2(Spots on Red) + (Spots on Green). Determine the pmf for the random variable. In particular f(6)
(3) Let X be a random variable with p.d.f 2 (3x+6) 15 then E(x) is 11 12 (b) 30 (c) 30 (d) (e) None of these 33 716
I roll a die with 10 faces numbered 0-9 and obtain a score X. What is E(X)? In order to obtain a random number between 0 and 99 I roll the die twice obtaining scores X and Y, then set Z = 10X + Y (i.e., the first roll determines the "tens", the second roll the "ones"). Is it true to say that E(Z) = 10E(X) + E(Y)?
3.Suppose that X and Y are independent random variables for which Var(X)=Var(Y)=3. Find the values of (a) Var(X-Y); (b) Var(2X-3Y+1).
Example 2.8. Suppose X is a random variable whose CDF is: 3 Fx(z) = lp1.00)(2) + 100.0)(2) +20.00)(2) + Ig0,(?) Determine the following: a) fx(1) b) fx(0.1) c) fx(100) d) P(х > 105) e) P(0 0.1)

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