Consider the following cumulative distribution function on N2 = [0, b], where b = ✓ln(1 + e-¹) + 1: е F(x) = e²²-¹ – e-¹, 0 ≤ x ≤ b. - Let X be a random real number in S. Compute the following probabilities: P(X ≤ 0.45) = P(X ≥ 0.85) = P(0.45 ≤ X ≤ 0.85) = Use the complement: X < 0.45 or X > 0.85, and your answers to the previous two parts. (hint: complement)
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![Consider the following cumulative distribution function on = [0, b], where b = √ln(1 + e−¹) +1:
S
F(x) = e²²-1
Let X be a random real number in S. Compute the following probabilities:
P(X ≤ 0.45) =
=
P(X ≥ 0.85)
P(0.45 ≤ X ≤ 0.85) =
Use the complement: X < 0.45 or X > 0.85, and your answers to the previous two parts.
=
(hint: complement)
- e e-¹, 0≤x≤ b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b2b0246-74c5-427f-bbae-6a253749f017%2F506c376a-318c-422c-8996-415b55f5892e%2F9ok68v_processed.png&w=3840&q=75)
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- Suppose (S, P) is a binomial distribution with n trials and probability of success p. Let X be the random variable X(k) = k³, where k is the number of successes. Calculate E[X].Suppose X is a discrete random variable which only takes on positive integer values. For the cumulative distribution function associated to X the following values are known: F(18)=0.4F(25)=0.44F(33)=0.5F(41)=0.53F(46)=0.56F(52)=kF(57)=0.64F(65)=0.67 Assuming that Pr[25<X≤52]=0.17, determine the value of k.Suppose X is a random variable of uniform distribution between 1 and 7. Find E(X)
- The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define Z:=√1-p²X + pY. Show that E[Z|Y] =pY.Let X; (i = 1, 2,..., n) be i.i.d. exponential random variables with E{X;} = 1/A. Let Y = mn{X1, X2,..., Xn}. What is the distribution of Y? (Compute P{Y > y}.) What is the distribution of Z = max{X1, X2, ..., Xn}? (Compute P{Z < z}.)
- Let Y1,..., Y, be i.i.d. random variables from the Weibull distribution f(y; 0) Σ (멤) exp ), y > 0. Show that ô = Li=1í is an unbiased estimator of 0. Is Ô an efficient estimaotr of 0?Given that X has the probability distribution f(x) = 1 for r 0, 1, 2,3, and 4. 16 Find the moment-generating function (MGF) of this random variable. Use the MGF to determine p. ' Use the MGF to determine u.Suppose X is a discrete random variable which only takes on positive integer values. For the cumulative distribution function associated to X the following values are known: F(23) 0.34 F(29) = =0.38 F(34) 0.42 F(39) 0.47 F(44) = 0.52 F(49) 0.55 F(56) = 0.61 = Determine Pr[29My Find the standard deviation of the discret probability dist x P(x) xp(x)) (x-M)² | (x-mipul 2 σ = √(x-M)² pxx) ટે О 0.21 10*0.21=0 /10-112 =. M= Exp(x) 1 0.30 1*0.3 = 0.3 2 0=49 EXP(X) =MLet X and Y denote the weights (in grams) of apples which are imported from two different locations: Peshawar (Pakistan) and Zanzibar (Tanzania), respectively. Suppose that X has Normal distribution N(148, 3); and Y has Normal distribution N(151, 4). One apple is randomly selected from each city. We assume independence between X and Y. • [[a)] Find the probability that the weight of the apple from Peshawar exceeds the weight of the one from Zanzibar • [(b)]A random sample of 36 apples is selected from those imported from Peshawar. Compute the probability that their sample mean will fall between 150 and 152. Paragraph BI Path: p pe here to search II !!!x has continuous random variable is nomally distributed and average 40, standard deviation 10. So what is the probability of P (30Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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