For what values c and α is the function p, defined by p(k) = {p(k) = ck^α for k = 1, 2, 3..... and p(k)=0 otherwise a probability mass function?
P(k) will be probability mass function only when
and k=1,2,3....n the P(k) is a probability mass function
For what values c and α is the function p, defined by p(k) = {p(k) =...
(a) Consider a Poisson distribution with probability mass function: еxp(- в)в+ P(X = k) =- k! which is defined for non-negative values of k. (Note that a numerical value of B is not provided). Find P(X <0). (i) (4 marks) Find P(X > 0). (ii) (4 marks) Find P(5 < X s7). (ii) (4 marks) 2.
The Poisson distribution with parameter λ has the mass function defined by p(x) = λ x e −λ/x! if x is a nonnegative integer (and 0 otherwise). Find the probability it assigns to each of the following sets: a. [0, 2) b. (−∞,1] c. (−∞,1.5] d. (−∞, 2) e. (−∞,2] f. (0.5, ∞) g. {0, 1, 2} Find the CDF of the uniform distribution on (0,1).
Answer number 3, please.
2. The probability mass function below is defined forx - 0, 1,2,3,... 32 f(x)- What is the probability for each of the following expressions? a) P(X 2) b) P(X S2) c) P(X>2) d) P(X2 1) Determine values of the cumulative distribution function for the random variable in the previous problem 3.
Consider the production function given by Q = l^α + k^α where α > 0. At what values of α does the production technology exhibit increasing, decreasing, or constant returns to scale? Prove your answer!
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5. The probability mass function of the discrete random l'is p()r fori 0,1, and 0 otherwise. If 0 <r< 1, what is k?
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Determine values of the cumulative distribution function for the random variable in the previous problem. 3. 2. The probability mass function below is defined for x 0, 1,2,3,.. fr 5 5 -56 What is the probability for each of the following expressions? a) P(X 2) b) P(XE 2) c) P(X> 2) d) P(X2 1)
2. Given k(2x + 3y) if a_ 0.1.2: у-0, 1. plx,y) - is a joint probability mass function(discrete case). a. What is k? b. Find the momen generating function Mx(t) c. Find the conditional probabilities P(Y X), P(Y 0X 1), P(X 1Y 0
2. Given k(2x + 3y) if a_ 0.1.2: у-0, 1. plx,y) - is a joint probability mass function(discrete case). a. What is k? b. Find the momen generating function Mx(t) c. Find the conditional probabilities P(Y X),...
The joint probability density function of X and Yis defined by f(, )0 elsewhere What is Pr(X Y K z,0 1)?
The joint probability density function of X and Yis defined by f(, )0 elsewhere What is Pr(X Y K z,0 1)?
Find the value of c for which p(x) defined below is a probability mass function: (a) p(x) = cx, x= 1,2,3. (b) p(x) = (-*, x= 1,2,3,...