given f(x)= (3/5).(2/5)x
then
a) p(x = 2) = (3/5). (2/5)2
= 0.096
parts a,b c given in the following images
2. The probability mass function below is defined for x 0, 1,2,3,.. fr 5 5 -56...
Previous Problem: 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)
PLEASE ANSWER NUMBER THREE (not number two) This problem (number 2) is only for reference. 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)
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.
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
Question 12: Let X and Y have the joint probability density function Find P(X>Y), P(X Y <1), and P(X < 0.5)
The probability mass function of a random variable X is given by Px(n)r n- (a) Find c (Hint: use the relationship that Ση_0 n-e) (b) Now assume λ = 2, find P(X = 0) (c) Find P(X>3)
2. For each p> 1, denote by || . || the norm in R" defined by: n || 2 || p = [f(x)}; where f(x) = 5:), Vx = ((1, ... , In) € R". i=1 For p > 1 and r* in the dual of R", consider the following optimization problem: n(x*) = sup|(2*, 2) : ||- ||| < 1] = sup[(x*, r) : f(x) < 1] 1 . Prove that n(x*) = || 2* ||g, where q> 1...
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