Suppose that three random variables x,„X,„X, fom a random sample from the uniform distribution on the interval [0,2], and they are independent. Determine the value of Е(2X, —3х, +х, -4). Var(2X, —3х, +х, —4) and E(2х, -зх, +х, —4)*|
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![Suppose that three random variables x,„X,„X, fom a random sample from the
uniform distribution on the interval [0,2], and they are independent.
Determine the value of
E(2X, –3X, +X,-4). Var(2X,–3X,+X, -4) and E(2x, –3X, +X, -4)°]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b1ac93b-2030-49ee-bbfa-587197c07896%2Fb683f60d-2e7b-49f0-85e9-f0cc38c1bdb3%2Fjcdy35_processed.png&w=3840&q=75)
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- Many people believe that the daily change in price of a company's stock in the stock market is a random variable with mean 0 and variance o² during the middle 2 months between 2 earning report dates when there is not much news released. That is, if Yn represents the closing price of the stock on the nth trading day of that period, then Yn = Yn-1+Xn, for 1 ≤ n ≤ 60, where X₁, X2,..., X60 are independent and identically distributed random variables with mean 0 and variance o². Suppose that the stock price at the beginning of the 2-month period is 100. If o = 2, what is the approximate probability that the stock's closing price on the 30th trading day will exceed 110, i.e., what is P(Y30 > 110)Suppose that one variable, x, is chosen randomly and uniformly from [0, 2], and another variable, y, is also chosen randomly and uniformly from [0, 4]. What is the probability that x≤y≤2x+1?The probability for x≤y≤2x+1 isSuppose that 36% of all voters prefer the Democratic candidate. Let X be the number of people who prefer the candidate when 21 people are surveyed at random. What is the distribution of X? X ~ ? B U N (,) Please show the following answers to 4 decimal places. What is the probability that exactly 7 voters who prefer the Democratic candidate in the survey? What is the probability that at most 7 voters who prefer the Democratic candidate in the survey? What is the probability that more than 7 voters who prefer the Democratic candidate in the survey? What is the probability that between 5 and 12 (including 5 and 12) voters who prefer the Democratic candidate in the survey?
- Suppose X~ Uniform [10, 50], find: P70 Variance (X)X ~ N(50, 12). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. 1 Give the distribution of X. (Enter an exact number as an integer, fraction, or decimal.) 2sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(X < 50) = 3Find the 40th percentile. (Round your answer to two decimal places.) 4Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(48 < X < 54) = 5 Give the distribution of ΣX. 6 Find the minimum value for the upper quartile for ΣX. (Round your answer to two decimal places.) 7Sketch the graph, shade the region, label and scale the horizontal axis for ΣX, and find the probability. (Round your answer to four decimal places.) P(1200 < ΣX < 1350) =An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.
- It was found that 85% of the students graduated from a technical university are employed within 6 months after graduation. A random sample of 20 graduated students were selected. If X the number of employed students, thus X~B(6,0.85) Select one: O True O FalseIf a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!X ~ N(50, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums. Part (e) Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(48 < X < 54) = Part (f) Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(13 < X < 46) = Part (g) Give the distribution of ΣX.ΣX ~ ,
- Suppose that a medical test has a 85% chance of detecting a disease if the person has it (P(PT|D)=0.85) and a 90% chance of correctly indicating that the disease is absent if the person really does not have the disease (P(NT|Dc=0.90). Suppose that 95% of the population does not have the disease P(Dc)=0.95 What is the probability that a randomly chosen person will test negative P(NT)?X ~ N(60, 14). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of averages. Let ΣX be the random variable of sums.Give the distribution of X. Sketch the graph, shade the region, label and scale the horizontal axis for X, and find the probability. (Round your answer to four decimal places.) P(X < 60) =.Find the 30th percentile.1. Given that X~N(39,32)A Random variable X is normally distributed and has a mean of 9 C Random variable X is not normally distributed and the mean is 39 B Random variable X is normally distributed and has a mean of 3 D Random variable X is normally distributed and the mean is 39
