Let x ~ Poisson(4). Determine: a) P(x = 1) b) P(x = 0) c) P(x < 2) d) P(x > 1) e) μx f) σx
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Let x ~ Poisson(4). Determine:
a) P(x = 1)
b) P(x = 0)
c) P(x < 2)
d) P(x > 1)
e) μx
f) σx
Step by step
Solved in 2 steps with 10 images
- (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}. Describe xNY.Suppose that Y, and Y, are uniformly distributed over the triangle shaded in the accompanying figure. y2 (0, 1) (-1, 0) (1, 0) (a) Find 6Find f, and f, and evaluate each at the given point. f(x, y) = e*y?, (In 9, 2) f,(x, y) = 1,x, v) = f,(In 9, 2) = f,(In 9, 2) =
- what is ?(R^2Y^3)?2 One hundred students take part in a school sports event. 70 students take part in track events (T), 62 students take part in field events (F) and 8 students take part in neither. a Construct a Venn diagram to show this information. b If a student is chosen at random, calculate: i P(T) iii P(F') ii P(T^F) iv P(TUF)2. Show that co cov (3₂) = 0
- Consider a random poker hand of 5 cards. Let X be the number of Hearts in this hand, and let Y be the number of Diamonds in this hand. Find Cov(X, Y). (Hint: rewriting in terms of indicator functions may be helpful.)Let P(A) = P(B) = and P(ANB) = . Find the following: /. (a) P(A¹). (b) P(A'N B'). (c) P(BnA'). (d) P(AUB').If X1, X2, ... , Xk have the multinomial distribution ofDefinition 8, show that the covariance of Xi and Xj is−nθiθj for i = 1, 2, ... , k, j = 1, 2, ... , k, and i Z j.
