G0o Suppose the random variable has the cdf 0, x < -3 F(z) = 12-3
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- Let random variable X be the number of users communicating with a cellular base station within a given time interval. Its PMF is :R1Cards 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.
- If is a random variable that has a uniform distribution on the interval [0, 10], then p(x+ 27) PX+ is equal to(3) Let X be a random variable with p.d.f. 2k 3x f(x)= ILet X be a random variable and c be a constant. Then Var(X+c) = Var(X), always. True FalseQ5 Let a discrete random variable Xhas values -1, 1, 2, and 3, with probabilities (1/4, 1/8, 1/8, 1/2) respectively. What is PDF of X? (WVith drawing) By using PDF of X, 2-p (1A 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)Q5Prob ... solve Q 1 & Q 2 please ?The random variable x is N(10,1). Find f(x(x-10)²<4).ans Theorem 9.3. Let X and Y be independent random variables with finite variances, and a, b ER. Then Var(aX) = a²Var (X), Var (X+Y) = VarX + Var Y, Var (ax + bY) = a²VarX + b²Var Y. sercise Prove the theorem. Remark 9.2. Independence is sufficient for the variance of the sum to be equal to the sum of the variances, but not necessary. Remark 9.3. Linearity should not hold, since variance is a quadratic quantity. Remark 9.4. Note, in particular, that Var (-X) = Var(X). This is as expected, since switching the sign should not alter the spread of the distribution.SEE MORE QUESTIONSRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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