l. Let wn > 0 and 〈 > 0. Show that s2 + 2(Wns+uậ = 0 has (a) complex roots when 0 < £1. (b) real and equal roots when ς-1, and real and distinct roots when ς > 1
please show the answers without work clearly
Minimize g = 3a5y Subject to 4x + y 2 18 12 24 > 0 Minimum is at IV IV IV IV
Consider the following two lotterics: L $200 with probability 0.7, 0 with probability 0.3, and L' $1200 with probability 0.1 and $0 with probability 0.9. Let xi and ru be the sure amounts of money the individ- ual finds indifferent to L and L' respectively. Show that if preferences are monoton e, the individual must prefer L to L' if and only if L>x
Prove that is an integer for all n > 0.
I need this equation's analytical solution with this
non-homogenous boundary conditions
=07 , 0 x L,120 where a = 0.013 L=1 Initial condition T(z,0) = 0 BCs are 70, t > 0) = 50 TL,t50
1.3 Let X є {-1, +1} denote the outcome of an toss of an unbiased coin. (That is, Pr(X +1]-Pr[X-_1] = 1/2.) say the coin in tossed 1000 times independently, and the correspoinding outcomes are denoted by X1,... , X1000 Give a good estimate of the chance that the average of the 1000 tosses exceeds the value 101 That is, give the best possible value of a, such that Pr(x, + X1000) > 10] 〈 α.
PROVE:
4. If f : R → R is a strictly increasing function, f(0) = 0, a > 0 and b > 0, then
Suppose that A1,A2,.., Ak are mutually exclusive events and P(B)>0. Prove that
n. 7. Let Xi, , Xn be iid ;0) =-e-r2/0 where x > 0. Sho w that θ=「x? is based on f (x efficient.
Consider the density: T- where σ2 > 0 is a fixed parameter. (a) Show that this is a valid density (b) Compute the CDF and its inverse