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- The PDF of a random variable is if x 4 f(x) = { a.) What is the value of A? 0, A (7+x)²² b.) What is the value of P(4 4, if ifJ 2 Uncorrelated random variables are not necessarily independent, however. A special situation occurs in the case of jointly Gaussian random variables. For the Gaussian case, uncorrelated random variables are also independent. I donot understand thses sentence. Please explain it through an example.The probability generating function for a random variable X is given by: 1 1,25 1 9x(z) =z2 + 1 -z20 710 + 2 P(X < 5 |X < 13) equals Select one: а. 0.8 b. 0.2 C. 1 d. 0.286 е. О
- Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.A deck has only 51 cards left, because a spade has been removed. From this deck, cards will be drawn at random, in succession, without replacement. Let Xi be a random variable representing the number of spades in the future i th draw. Calculate the following, and present your answer with 5 digits after the decimal point: Prob(X1 + ... + X7 = 3) = [1]An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (*) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of heads in each outcome. For example, if the outcome is ttt, then N (ttt) = 0. Suppose that the random variable X is defined in terms of N as follows: X=2N -2. The values of X are given in the table below. Outcome ttt hth tht htt thh hhh hht tth Value of X -2 2 0 0 2 4 2 0 Calculate the probabilities P(X=*) of the probability distribution of X. First, fill in the first row with the valuesof X. Then fill in the appropriate probabilities in the second row. Value x of X ___ ___ ___ ___ P(x=x) ___ ___ ___ ___
- If Z is approximately N(0,1), the probability, after "Z lies in" between -1.50 and 2.37, is:An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is tth, then N (tth)=2. Suppose that the random variable X is defined in terms of N as follows: X=N²-2N-2. The values of X are given in the table below. Outcome ttt htt hhh tht tth hth hht thh Value of X 1 -2 -2 -2 -2 -3 -3 -3 Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 0 0 0 0 00 X ŚSolve Q21
- In a box containing 8 red balls, 8 green balls and 8 blue balls where 3 balls will be drawn in random with replacement, let G be the random variable representing the number of green balls chosen. What is f(0)? a. 4/9 b. 8/27 c. 1/27 d. 02. The number of meteors found by a radar system in any 30-second interval under specified a. What is the probability that at least one meteor is found in a one-minute interval? ne meteors appear randomly b. Determine x such that the probability no meteor is found in x-minute interval is 0.02. UTM M UTM UTM c. If there is no meteor appear after two-minute interval, what is the probability that it UTM will appear in the next one and a half-minute interval? m UTMPavan