If random variable A is distributed N(3, 8) and random variable B is distributed N(−3, 10), what is the distribution of mA + nB for some constants m and n?
If random variable A is distributed N(3, 8) and random variable B is distributed N(−3, 10),...
Problem 5: 10 points Assume that a discrete random variable, N, is Poisson distributed with the rate, λ = 3. Given N = n, the random variable, X, conditionally has the binomial distribution, Bin [N +1, 0.4] 1. Evaluate the marginal expectation of X. 2. Evaluate the marginal variance of X
L.11) Brand name distributions a) Give an example of a normally distributed random variable. b) Give an example of an exponentially distributed random variable. c) Give an example of a random variable with the Weibull distribution. d) Give an example of a random variable with the Pareto distribution. L.4) Sample means from BinomialDist[1, p] IfXl. X2. X3, Xn are independent random samples from a random variable with the BinomialDist[1, p] distribution, then what normal cumulative distribution function do you use...
Question # 10 A random variable (RV) x is uniformly-distributed from a to b. Given that: p(a sx b) 2 and the median v alue of the RV is equal to: 5. Hence, determine the values of a and b. (Note: The median divides the distribution such that: CDF to its left CDF to its right 0.5) Answer-hints: a-4.75 and b-5.25
Problem 8 (10 points). Let X be the random variable with the geometric distribution with parameter 0 <p <1. (1) For any integer n > 0, find P(X >n). (2) Show that for any integers m > 0 and n > 0, P(X n + m X > m) = P(X>n) (This is called memoryless property since this conditional probability does not depend on m. Dobs inta T obabilita ndomlu abonn liaht bulb indofootin W
Problem 2: Let X be a binomially distributed random variable based on n 10 trials with success probability p 0.3. a) Compute P(X 3 8), P(x-7 and PX> 6) by hand, showing your work.
QUESTION 9 Y is a random variable that is distributed N(5,12.96). Find k such that Prob(Y< 2.012 OR Y> k) 0.9356 QUESTION 10 Y is a random variable that is distributed N(-2,17.64). Find k such that Prob(Y <-10.19 OR Y> k)-0.0444 QUESTION 11 Y is a random variable that is distributed N(2,104.04). FIind Prob(-27.784 < Y<7.916).
Suppose X ~ N (10, 6). This says that x is a normally distributed random variable with mean μ = 10 and standard deviation σ = 6. Suppose x = 20, then x= 20 means that it is: a) 1.67 above mean b) 1.67 below mean c) 0.67 above mean d) 0.67 below mean
2ND TEST IN PROBABILITY THEORY AND STATISTICS Variant 8 1. X is a continuous random variable with the cumulative distribution function if x<0 F(x)ax2 0.1x if osxs 20 if x> 20 0 Find 1) the coefficient a; 2) P 10); 3) P(X<30). 2. The result of some measurement X is normally distributed with parameters 184 and 8. Compute the probability that variable X takes value from interval (170;180) at least once in 5 experiments 3. Two independent random variables X...
The random variable X is distributed as a Pareto distribution with parameters α = 3, θ. E[X] = 1. The random variable Y = 2X. Calculate V ar(Y )
Problem 8: 10 points Assume that a lifetime random variable (T) is exponentially distributed with the intensity λ 〉 0. 1. Find conditional variance, Var TIT〉 u] . 2. Find conditional second moment, E T IT ]