Let X be a random number with probability density function 1. Find the expectation E[X] of X. 2. Find the variance Var(X) of X. fx(x) = 256x²e-8 if x ≥ 0, 0 Otherwise.
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Find the expectation and varience of X.
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- Match the probabilities with the commands. In the answers, the first command stated is for EXCEL and the second is for the Tl calculator. 1. P(X = a) 2. P(X ≤ a) 3. P(X a) 5. P(X> a) 1. 2. 3. 4. [Choose ] [Choose ] =BINOM.DIST(r,n,p,TRUE) or binomcdf(n,p,r) =BINOM.DIST(r-1,n,p,TRUE) or binomcdf(n,p,r-1) -1- BINOM.DIST(r.n.p,TRUE) or 1 -binomcdf(n.p.r) 1- BINOM.DIST(r-1.n.p.TRUE) or 1 -binomcdf(n.p.r-1) -BINOM.DIST(r.n.p.FALSE) or binompdf(n.p.r)assume that Pr[A] = 0.45, Pr[B] = 0.35, and Pr[A n B] = 0.25. Compute the following conditional probabilities: (1) Pr[A|B] = (2) Pr[B|A] =A probability distribution gives the possible values of the random variable and the probabilities of each random variable. Probabilities have to be between 0 and 1. The sum of all the probabilities has to be 1. Additionally, the different values for the random variable are disjoint possibilities. In other words P(Xa and X - b) = 0 if a and b are different outcomes. Fill in the missing value for the probability distribution. P(X) 0.151 X 3 4 5 What is P(X-6)? 0.04 0.026 ?
- Answer all 4 parts correctly please. I will rate accordingly.Sarah and Thomas are going bowling. The probability that Sarah scores more than 175 is 0.5 , and the probability that Thomas scores more than 175 is 0.1 . Their scores are independent. Round your answers to four decimal places, if necessary. (a) Find the probability that both score more than 175 . (b) Given that Thomas scores more than 175 , the probability that Sarah scores higher than Thomas is 0.4 . Find the probability that Thomas scores more than 175 and Sarah scores higher than Thomas.A student will take an exam that lasts a maximum of one hour. The probability that the student finishes the exam before x hours is x / 2, 0 ≤x≤1. If it is known that the student is still taking the exam at the end of 0.75 hours, what is the probability that the student will use the entire hour?
- Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x(girls) P(x) x(girls)| P(x) |x(girls)| P(x) 0.000 0.122 10 0.061 1 0.001 0.183 11 0.022 2 0.006 7 0.210 12 0.006 3 0.022 8 0.183 13 0.001 4 0.061 9 0.122 14 0.000 Find the probability of selecting 12 or more girls. 0.001 O 0.022 0.006 O 0.007The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.45, the analogous probability for the second signal is 0.5, and the probability that he must stop at at least one of the two signals is 0.9. (a) What is the probability that he must stop at both signals? X (b) What is the probability that he must stop at the first signal but not at the second one? X (c) What is the probability that he must stop at exactly one signal?A drawer holds purple socks and yellow socks. If n socks are taken out of the drawer at random, the probability that all are yellow is 1/2. What is the smallest possible number of socks in the drawer (as a function of n)?
- Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities 0.35, 0.15, 0.35, and 0.15, respectively. (a) Calculate E(X) and then E(5 - X). E(X) E(5-X) = (b) Would the repair facility be better off charging a flat fee of $70 or else the amount $ 150 (5-X) The repair facility ---Select--- be better off charging a flat fee of $70 because E ]= 150 (5-X)] ? Note: It is not generally true that : E ( =) = E(Y)IToday's practice The following circuit operates if and only if there is a path of functional devices from the left to the right. Assume the devices fail independently and that the probability of failure for each device is 0.9. What is the probability that the circuit operates? TI 3 T2 4. 5.Assume that we flip a coin until a 2nd head is seen. Let X be the number of flips up until and including the flip that has the 2nd head. What is the pmf and expectation of X?