The variable X has 5 values: 2, 4, 1, 0, 5.
A random variable has the following distribution X 0 1 2 3 4 5 6 7 8 P(x) k 3k 5k 7k 9k 11k 13k 15k 17k Find the value of k Find P( X < 4) , P( 0 < x < 4) Find the smallest value of x for which P( X less then or equal to k) > 0.5?
Discrete random variable X has possible values 2, 6, 10, 14, 18, and 22. Continuous random variable Y has density function f(y) = y/288, if 0 < y < 24 and f(y) = 0 otherwise. If Y is a good approximation for X, find Pr[6 ≤ X ≤ 18].1/41/35/72/31
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5. The values of a variable X are: 1,3,9,5, 4, 2 Compute the following: x3 {X? [(x - 2) XS
The random variable X takes only the values 0, ±1, ±2. In addition, it is known that P(-1 <X <2) 0.2 P(X = 0) = 0.05 PCI 1) = 0.35 P(X 2) = P(X = 1 or-1) (a) Find the probability distribution of X (b) Compute E[X]
4) Suppose a random variable X has theprobability distribution with a: o 1 -2 0 1 2 0.3 0.1 p 0.4 . then p - ,P(X2 22) = ,, and E(X) = - 5) Suppose X~Bin(10,0.4), Y-2X+5, then E(Y) = ,Var(Y) 6) Suppose X-NC-3,4) and Y~N(2,9), X and Y are independent, then Var(X-2Y)
Let X be a discrete random variable taking integer values 1, 2, ..., 10. It is also known that: P(X < 4) = 0.57, PCX 2 4) = 0.71. Then P(X = 4) = A: 0.14|B: 0.28 |C: 0.45 OD: 0.64|E: 0.73 OF: 0.95 Submit Answer Tries 0/5
The Bernoulli random variable takes values 0 and 1, and has probability function f(x) = px (1 − p)1−x(a) By calculating f(0) and f(1), give a practical example of a Bernoulli experiment, and a Bernoulli random variable. (b) Calculate the mean and variance of the Bernoulli random variable.
A function, f. has the following table of values: 4 6 X 0 f(x) 2 23 43 -2 - 1 -4 1 Approximate] пом. Approximate f(x)d.r using a Riemann sum with 2 rectangles and midpoints. 6 0 -2 4 O2 Question 4(5 points) ✓ Saved firmaland itsdaluritius Р w o 19 MacBou
Evaluate the piecewise function at the given values of the independent variable. x +4 if x 2 -4 g(x) = (x+4) if x <-4 (a) g(0)=□ (b) g(-7)=□ (c) g(1)=□
Consider the following frequency table of observations on the random variable X. Values 0 1 2 3 4 5 Observed Frequency 8 25 22 21 16 8 (a) Based on these 100 observations, is a Poisson distribution with a mean of 2.4 an appropriate model? Perform a goodness-of-fit procedure with α=0.05. Which of the following is the correct conclusion? (b) Which of the following are the correct bounds on the P-value for this test.