2. Suppose that Z, and Z, have a joint probability density function given by f(Z,,2) =3(1- z,2), Osz s1, 0sz51 2,z2), 0, elsewhere a) What is the marginal distribution of Z,. b) Find P(Z, s)
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- and Let Let X ~ N(μ, E), where Σ μl = = = (:). LL2L 121 12 14121 (X3 + X₁) r- (x²+x2) Y 2X2 = X3-X₁ i) What is the distribution of Y? ii) Which components of Y are independent of each other?3. If the probability density function of random variable is given by f(x)=1/sechx 1 ≤ x ≤ 2 a) Find the mean b) Find the total areaThe salaries of workers represent uniform distributed random variable from1000 to 2000 dollars. a) Construct corresponding probability density function. b) Find the probability, that the salary of randomly selected worker is not less than 1400 dollars.
- 3) For known k ≥ 2 show that the negative binomial distribution with probability mass function, f(y, k, μ) y = 0, 1, 2, .. = - 1 k k k (³ + k − ¹) (¹ − µ 4 k)" (1² k) " 1 Y + 1 belongs to the exponential family of distributions. Find the natural parameter for this distribution.The random variable X has the geometric distribution with probability mass function (pmf) Py(x) = q*p. x = 0,1, 2, ... 0 x). |A7 The random variable X has the binomial distribution with probability mass function () p*(1 - p)²-*, x = 0, 1,2; 0I need the answer quicklyplz dont copy the answers from others, rly need it to studythe proportion of spectrum shift that a certain atomic particle produces is The joint density for the random variable (X,Y), where X is the unit temperature change and Y is f(x) = 2 100 xy² 0Forthe following joint distribution P(xy), find E[X^2]. P (X, Y) Y- -1 Y= 0 Y=1 Y=2 |0,1 0,3 Х-1 0,05 0,1 X- 2 0,25 0,1 0,05 0,05 O A) 1.575 O B) 1.85 C) 2.5 O D) 2.35 O E) 1.65SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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