1. Use R's "pbinom()" function to verify Chebyshev's inequality for k=2 and k-3 when X follows Binomial(30, 0.2).

Q: . What is the coefficient of a" in (2 – x)"?

A:

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

A:

Q: b. Маx z %3DX1 + X2 s.t. 2x1 + x2 < 20 X1 +3x2 < 15 X2 < 4 X1, X2 2 0

A:

Q: PROB.NO. 4 VERIFY THAT (X - 3 )(X - 21) = (X - 21 )(X - 3) = Xx - 5X + 61 FOR [i 2 0] X =0 30 0 0 4

A: To verify the given expression is followed by matrix X .

Q: Show that if (B) (C) N N then the value of neither x nor y can exceed 1/4. (A) N = X, 2x, = 3x and…

A:

Q: 4. Let h(r) = 5 x 6 20 x²3x18 Find all values of N for which h(N) = 3.

A:

Q: 18. 2. If f(x)=3x²-7 for all real numbers x, which of the following is equal to f(3) +ƒ(4)² A. S(0)…

A:

Q: For constants o > 0 and a > 0, the function aoª p(æ) = xa+1³ where x > 0, is called a Pareto…

A: c) From part b, A=∫σ∞xp(x)dx Here, p(x)=ασαxα+1 And A=∫σ∞xp(x)dx is defined for the condition…

Q: Q2. P(A) = 0.42, P(B|A) = 0.66 and P(B|A’) = 0.25. Find the following – P(A’), P(B’|A), P(B’|A’),…

A: We have given information, P(A)=0.42 PB|A=0.66 P(B|A')=0.25

Q: evaluate L-1 { t/(s-2)(s+3)}

A: By using partial fraction and table of Laplace transform we solve the given problem as follows :

Q: 9. Solve In (x+5) 2 2. O A. (x | x 2 12.3891} B. (x | x 2 2.3891} O C. (x |xs 12.3891} O D. {x |x s…

A: Given:         ln(x+5)≥2

Q: Suppose P(Xi=1)=pi=1-P(Xi=0),  i=1,2 if p1> p2 show that X1>( greater than equal to (st)) X2

A:

Q: a. The remainder of P(x) = 2x' +mx? –7 when it is divided by x+2 is 6 greater than when it is…

A:

Q: 10. Suppose X-N (3.2) Find P (22}, P(X>3)

A: Given that v  X ~ N ( 3, 22 )  i.e. μ = 3 ? = 2 By using standard normal distribution we solve this…

Q: Verify Mean Value Theorem for the function 3x? - 4x +5 in [-1,1]

A:

Q: Which function grows faster as O x → +∞ ? 3x¹ + 2x³ + 3x² +1 x³ ln(x² + 1)

A:

Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: 1. Let k and n be non-negative integers. (a) What does the function pr(n) count? (b) Show that the…

A: k and n are :Two non-negative integers.

Q: Denote owl and wood rat populations in a particular area at time k by xk LK Rk where k is the time…

A:

Q: for Q1. a. howd you get k=3 from the j <- 1 to n^2 statement? shouldn't it be k=2?

A: Given that From the equation * The recurrence relation is T(n)=25Tn5+Θ(n3)T(n)=25T(n5)+Θ(n3)…

Q: Determine the interval of convergence for € (-1)" n! (x-5)" ΑΞΟ 34

A:

Q: lex. min. {g, (x), g₂ (x)} 9₁ (x): -2x1 - x₂ ≥ 9 92 (x): X₁ X1 - 2x₂ ≥ 10 st. 2x1 + 5x2 ≤ 16 6x₁ +…

A: