Consider a random variable X with the following probability mass function P(X=0)=0.25, P(X=5)=0.5, P(X=12)=0.25. What is the expected value (or mean) of X?
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Consider a random variable X with the following probability mass function P(X=0)=0.25, P(X=5)=0.5, P(X=12)=0.25. What is...
Consider a random variable X, that takes values 0 and 1 with probabilities P(0) = P(1) = 0.5. Then, X = 0 with probability 0.5 and X = 1 with probability 0.5. What is the expected value of X? 0 0.25 0.5 1
The probability mass function for the discrete random variable X is p(X=0)=0.13; p(X=1)=0.31; p(X=2)=m. What is the expected value of X? Hint: First compute m, then find the expectation of X. Round your answer to the nearest hundredth.
Consider a discrete random variable X with the probability mass function p X ( x ) = x/C , x = 3, 4, 5, 6, 7, zero elsewhere. consider Y = g( X ) = 100/(x^2+1) . b) Find the probability distribution of Y.
5 Consider a discrete random variable X with the probability mass function rp(x) Consider Y = g( X ) =- 0.2 0.4 0.3 0.1 a) Find the probability distribution of Y. b Find the expected value of Y, E(Y). Does μ Y equal to g(Hy )? 4
5. Consider the discrete random variable X with probability mass function p.) = (3/30 for r=1 6/30 for r= 2 8/30 for r=3 7/30 for r = 4 4/30 for r = 5 2/30 for r= 6 10 otherwise. You may find it helpful to use a table with columns for I, Px(), 2. Px(2), and r.Px() to keep track of your computations. Do not round off-express all values as rational fractions. a) Find the probability P(X<3. b) Find the...
sc I The discrete random variable X has the following probability mass function: P(X = x) = kx for the values of x = 2,4 and 5 only. Find the i. value of k. expected value and the variance of X. iii. cumulative distribution function of X, F(x).
Question 4. [5 marksi Let Xbe a random variable with probability mass function (pmf) A-p for -1, 2,... and zero elsewhere (whereq-1-p, 0 <p< (a) Find the moment generating function (mg ofX. C11 (b) Using the result in (a) or otherwise find the expected value and variance of X. C23 (c) Let X, X,., X, be independent random variables all with the pmf fix) above, and let Find the mgf and the cumulant generating function of Y.
The following mass function describes the distribution for a random variable x: p(x)=0. x={1,2,3,...} (the upper bound of x is ) a) What is the probability x=5? b) What is the probability x ≥ 2? c) What is the probability x=1.5
5.Consider a discrete random variable X with the probability mass function xp(x) Consider Y-g(X) 0.2 0.4 0.3 0.1 a)Find the probability distribution of Y b) Find the expected value of Y, E(Y) Does μ Y equal to g(μx)? 4
For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)