3. 43 Let A= Find nullity A") 1 8 --3 0 5

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

Q: (c) P(\X| > 3) (d) P(|X – 5| > 3)

A: We have given that.   X~N( μ , ?^2 )   μ=5 , ? =1   Z-score =( x - μ )/?

Q: Let {(=) = In ="(z +2)*(z² + 9)] f'(x) =

A:

Q: (4) State which of the following statements are true, vacuously true, or false. (a) (A-B)' = A' -…

A:

Q: 10. If w is FALSE, x is TRUE, and y is FALSE, what is ((w OR Y') AND (x' AND y')') OR ((w OR y') AND…

A: Given :If w is FALSE, x is TRUE, and y is FALSE.To find : ((w OR y') AND (x' AND y')') OR ((w OR…

Q: ·C) - G) + G)-G) + +-1 - Prove that for any positive integer n, 0.

A: Use simple property of combination.

Q: Q1 If A 010 1 Par API AYA² KA ナ show That:

A: If , show that .

Q: 1 2 2 4 Let A = 2 1 1 5 ], What is A'? 2 4 2

A:

Q: 6.) Derike the binomial idendity nent) (un-) C Hint: For mzz, c^)+2(^) +m?]

A: To derive the binomial identity22+42+62+.........+2n2=nn+14n-16

Q: 12 3 n +2 (b) 2 = 2 – 2n + ..+ 22 23 2n lia on intege

A: (b)  To prove : 12+222+323+.....+n2n=2-n+22n for all n≥1   For n=1,  LHS : 12 RHS : 2-1+22=12= LHS…

Q: 17. Let P1.Pn be positive real numbers such that P1+ + Pn=1. (a) Prove the following: @P² ≥ (ii)…

A:

Q: (3x* – 1) dx + x°dy = 0; when x = 1, y = 1

A:

Q: Theorem = 7 K 51 M 25

A:

Q: 9. Let X Bin(4,.30), compute a. P(X=0) b. P(X= 1) C. P(X= 4)

A: Given that  Success of probability p=0.3 , q=1-p=0.7 Number of trials n=4 X~binomial (n,p)…

Q: 7.2.2 Fibonacci Numbers Denote the kth Fibonacci number as F. These numbers are defined by the rule…

A: We have to explain all the marked steps .

Q: Let x, y E N, determine each of following statemen is true or false (N means Natural number, natural…

A:

Q: 7.2.2 Fibonacci Numbers Denote the kth Fibonacci number as Fk. These numbers are defined by the rule…

A: The purple expressions are explained in detailed in below strps.

Q: & 18) Vaing showj that the idently in

A: Using the identity 1+x2n=1+xn1+xn,                . . . (1) we want to show that 2nn=∑k=0nnk2.…

Q: 4(-1)" Σ 3) Estimate 2N 1 correct to one decimal place. N-1

A:

Q: 5(x+1) =x+1 if x = 1. O True O False

A: By solving this equation we get,