Question 1. A Discrete Distribution - PME Verify that p(x) is a probability mass function (pmf)...
he cumulative distribution function (cdf), F(z), of a discrete ran- om variable X with pmf f(x) is defined by F(x) P(X < x). Example: Suppose the random variable X has the following probability distribution: 123 45 fx 0.3 0.15 0.05 0.2 0.3 Find the cdf for this random variable
2. Consider a discrete random variable X with mean u = 4.9 and probability distribution function p(x) given in the table below. Find the values a and b and calculate the variance o p(x) 0.25 5 6 0.35
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).
1. (Lec 6 & 7 discrete R.V., 16 pts) The pmf (probability mass function) of a random variable X is shown below: -2 0.2 Let A be the event that X is less than 0. .ן 0.4 otherwise px(x) 0.1 0.1 (a) Find the value of the constant a nd ElI and omai pmf of X given A (c) Find the conditional pmf of X given A. (d) Find E(X[A] and Var[X[A]. (e) Let Y2X 3. Find the pmf of...
how to answer this question? The probability mass function (pmf) for the Poisson distribution can be regarded as a limiting form of the binomial pmf if n o and p 0 with np = fi constant. (a) Suppose that 1% of all transistors produced by a certain company are defective. 100 of these chips are selected from the assembly line, Calculate the probability that exactly three of the chips are defective using both a binomial distribution and a Poisson distribution....
Problem 1. Let X be a discrete random variable with values -2,0,1,5 urith pmf (a) Verify that the probabilities do define a pmf (probability mass function) ( b) Compute the mean of X , i.e., μ -E(X) (c) Compute the standard deviation of X, i.e., σ- Nar(X)
Cumulative distribution function The probability distribution of a discrete random variable X is given below: Value x of X P(x-x) 0.24 0.11 -2 0.26 0.11 Let Fx be the cumulative distribution function of X. Compute the following: X 5 ? 18+ (-2) - Px (-4) = 0
2.1 Let X be a discrete random variable with the following probability distribution Xi 0 2 4 6 7 P(X = xi) 0.15 0.2 0.1 0.25 0.3 a) find P(X = 2 given that X < 5) b) if Y = (2 - X)2 , i. Construct the probability distribution of Y. ii. Find the expected value of Y iii. Find the variance of Y
he cumulative distribution function of X is given by 10 1,x2 3.5 Is X a discrete or continuous random variable? Give the appropriate probability mass or density function of X based on your answer
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.