Let ? be a branching process, with ?0=2 and family size distribution ? ∼ Bin(2,3/4). What...

Let ? be a branching process, with ?0=2 and family size distribution ? ∼ Bin(2,3/4). What is the probability that the process will eventually die out?

Expert Solution

orchestra answered 1 year ago

Let X~BIN(40,0.1). Let Y=max(0,x-3). FindE[Y].

2. Let X ~ Pois (λ) λ > 0 a. Show explicitly that this family is...

2. Let X ~ Pois (λ) λ > 0 a. Show explicitly that this family is “very regular,” that is, that R0,R1,R2,R3,R4 hold. R 0 - different parameter values have different functions. R1 - parameter space does not contain its own endpoints. R 2. - the set of points x where f (x, λ) is not zero and should not depend on λ . R 3. One derivative can be found with respect to λ. R 4. Two derivatives can...

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let...

Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let ?? be the ?-th smallest among {?1, ?2, ?3}. Find the variance of ?2, and the covariance between the median ?2 and the sample mean ? = 1 3 (?1 + ?2 + ?3).

Let X ∼ Normal(0, σ^2 ). (a) Find the distribution of X^2/σ^2 . (Hint: It is...

Let X ∼ Normal(0, σ^2 ). (a) Find the distribution of X^2/σ^2 . (Hint: It is a pivot quantity.) (b) Give an interval (L, U), where U and L are based on X, such that P(L < σ^2 < U) = 0.95. (c) Give an upper bound U based on X such that P(σ^2 < U) = 0.95. (d) Give a lower bound L based on X such that P(L < σ^2 ) = 0.95

Let A = [ 0 2 0 1 0 2 0 1 0 ]  . (a)...

Let A = [ 0 2 0 1 0 2 0 1 0 ]  . (a) Find the eigenvalues of A and bases of the corresponding eigenspaces. (b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line. (c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist. (d) Write down explicitly...

Let X be a continuous random variable that has a uniform distribution between 0 and 2...

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(2) Let ωn := e2πi/n for n = 2,3,.... (a) Show that the n’th roots of...

(2) Let ωn := e2πi/n for n = 2,3,.... (a) Show that the n’th roots of unity (i.e. the solutions to zn = 1) are ωnk fork=0,1,...,n−1. (b) Show that these sum to zero, i.e. 1+ω +ω2 +···+ωn−1 =0.nnn (c) Let z◦ = r◦eiθ◦ be a given non-zero complex number. Show that the n’th roots of z◦ are c◦ωnk fork=0,1,...,n−1 where c◦ := √n r◦eiθ◦/n.

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the eigenvalues of A and bases of the corresponding eigenspaces. (b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line. (c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist. (d) Write down explicitly a diagonalizing...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the...

Let A = 0 2 0 1 0 2 0 1 0 . (a) Find the eigenvalues of A and bases of the corresponding eigenspaces. (b) Which of the eigenspaces is a line through the origin? Write down two vectors parallel to this line. (c) Find a plane W ⊂ R 3 such that for any w ∈ W one has Aw ∈ W , or explain why such a plain does not exist. (d) Write down explicitly a diagonalizing...

2. Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]....

2. Let ?1, ?2, ?3 be 3 independent random variables with uniform distribution on [0, 1]. Let ?? be the ?-th smallest among {?1, ?2, ?3}. Find the variance of ?2, and the covariance between the median ?2 and the sample mean ? = 1 3 (?1 + ?2 + ?3).

Question

Let ? be a branching process, with ?0=2 and family size distribution ? ∼ Bin(2,3/4). What...

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