Use the PGF g(z) = (1 − p + pz)3 to determine the corresponding PMF and then state which distribution it has and state the parameters.
Use the PGF g(z) = (1 − p + pz)3 to determine the corresponding PMF and...
(f) Find the conditional pmf of X given Z. Identify this
conditional distribution as a distribution known in class, and
give
the explicit parameters for the known distribution.
(g) Find the conditional expectation of X given Z.
2. (Lec 13 &15 & 16 pairs of discrete R.V., conditional pmf and conditional moments, 17 pts) We are studying the flow of packets at a switch, which receives packets from two transmission paths, during a given period of time. Let X and...
15. Let X1, . . . , Xn be id from pmf p(z; θ)-(1-0)"-10; ;z=1,2, 3, ,and 0 < θ < 1. (a) Find the maximum likelihood estimator of θ (b) Find the maximum likelihood estimate of θ using the observed sample of 5,8,11.
please solve this questions using matlab.
tu 3 Countries over Exercise # 2: Plot the probability mass function (PMF) and the cumulative distribution function (CDF) of 3 random variables following (1) binomial distribution [p,n), (2) a geometric distribution [pl, and (3) Poisson distribution [a]. You have to consider two sets of parameters per distribution which can be chosen arbitrarily. The following steps can be followed: Setp1: Establish two sets of parameters of the distribution: For Geometric and Poisson distributions take...
Suppose that PX=.25, PZ=.4, P[X|Z] = .3. What is a) P[EUF] b) P[F|E]
3. Use the probability generating function Px)(s) to find (a) E[X(10)] (b) VarX(10)] (c) P(X(5)-2) . ( 4.2 Probability Generating Functions The probability generating function (PGF) is a useful tool for dealing with discrete random variables taking values 0,1, 2, Its particular strength is that it gives us an easy way of characterizing the distribution of X +Y when X and Y are independent In general it is difficult to find the distribution of a sum using the traditional probability...
4. Suppose X has a discrete uniform distribution: the distribution function of X 5. A random variable Z has the pmf bclow. P (X-х,)-1 , is|2 n. Find 0 Pz(z) 0.20 0.16 0.4 a (1) What is thevalue of a ? (2) What is P(l S Z <3)? (3) What is Fz (1.7)? 6.
Question 1. A Discrete Distribution - PME Verify that p(x) is a probability mass function (pmf) and calculate the following for a random variable X with this pmf 1.25 1.5 | 1.7522.45 p(x) 0.25 0.35 0.1 0.150.15 (a) P(X S 2) (b) P(X 1.65) (c) P(X = 1.5) (d) P(X<1.3 or X 221) e) The mean (f) The variance. (g) Sketch the cumulative distribution function (edf). Note that it exhibits jumps and is a right continuous function.
Consider the following pmf: p(x)- .25 for x - 1, 2, 3, 4 Determine the variance of the random variable, X. C. 15/12 O infinity 8/12 O9/12
25.) Find the z-score corresponding to the given value and use
the z-score to determine whether the value is unusual. Round the z
score to the nearest tenth if necessary. Show work for finding z
score
26. Identify which of these types of sampling is used
Find the z-score corresponding to the given value and use the Z-score to determine whether the value is unusual. Round the z-score to the nearest tenth if necessary. You must show your work for...
(a) Calculate the P and T values for which H2(g) is in a corresponding state to CH (g) at 10.0 bar and 310 K. The critical constants are the following: P.(H2)- 12.93 bar, T(H2) 32.98 K P (CH) 45.99 bar, T(CH4) 190.56 K. (b) Considering how the critical constants T and P, are related to the van der Waal's constants a and b (see formulas on back page), which gas do you conclude has stronger intermolecular attractive forces? (a) Calculate...