1-1 Q2: Let A = Find 1 1. ||4|| . L- 2. ||4| . 3. p(A).

Q: {X> 3} fX | {X> 3} (

A: X ∼ exp (λ) PX>xX>3=PX>xX>3   ; X>30                         ; otherwise

Q: Q2/Let X-N(4,9). Find (a) P(1 2). (c) P(|X-21 >5)

A:

Q: 19. Let f(x) = e*. Then, for all n, %3D f(n) (x) = e* and f(n)(0) = 1 It follows that T„(x) = 1+…

A: We have given;

Q: 6) Suppose z,=4¿ and z,=32 & Z2 Give Z1 7) Give the value of 5! and also show the calculation done…

A: as per our norms we are allowed to solve one question at a time.  Kindly repost the remaining…

Q: 1. (a) If f(n) = 0 (g(n)) then is g(n) = Q(f(n))? %3D

A: Big O, big Θ, and big Ω notations are very important in studying the time complexity and asymptotic…

Q: 2 10 Q(1) Let 4 0 7+x -3 find the value of x that makes det A = 0. 4

A:

Q: -145 2. find least 0అ కావులి Sంఖనాుంది spcave Axz b A z] 1 -4 1 1 2. 2. enter xas a Coloumn ve

A: Given that, AX=b A=1-4010012-1121,   b=3134 The least square solution to the system AX=b is the…

Q: (a) an = }(n² + n). (b) an = 2an-1 – an-2 with ao = 0 and aj = 1. (c) an = nan-1 with ao = 1. %3D

A:

Q: 7. If [G: H] = 2, prove that gH = Hg (18 from 6.5)

A:

Q: n-1 For all n > 2, 4+ 3n4" – 4n+1 - j=1 9.

A:

Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…

Q: (27) Let X = P(2) and - E(5-5x) find 2.

A: The properties of expectation an variance is E(aX+b)=aE(X)+bvar(aX+b)=a2var(X) 27) The expectation…

Q: (c) Two real numbers X and Y are chosen at random in the interval (0, 1). Compute the probability…

A: Let's assume that set of numbers X,Y|X,Y∈0,1 form a unit square, whose vertices are (0, 0), (0, 1),…

Q: 3. Given n > 1, let S = E-1: Show that S, is not k=1 _k° an integer.

A: We are given that   Sn = ∑k=1n1/k   and n>1              ..(i) We have to show that Sn  is not an…

Q: :""n e Z*, if n³ = 3k for some k E Z, then n = 3q for some q E Z." %| %3D

A:

Q: 12. Find all values of t for which - 1 -2 1+2 0 0 -1 = 0. 0 1+1

A:

Q: 2 Delermire if fW=x s is even, odd neither.

A: As we know that a function f(x) will be  1. even function if f(x)=f(-x)  2. Odd function if…

Q: 63. Given n nonzero numbers o1,...,on, show that the minimum value of S(x1....,xn) = xfo7 +..+ x…

A:

Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

A:

Q: Q4/ Let S(x)=- x-1 S(x)= and g(x)=1+ Find (g(x) and ag)(x).

A: We define two functions: f(x) = x/(x - 1)  g(x) = 1 + 1/x = (x + 1)/x Then, we have to find the…

Q: 2x-3 for *く-S メ+4 %3D ーメ+3 for マ-S メ+2 for x) -5 メ+ヒ find *ビ" し 1n for order f(x) to メ- -5

A:

Q: -4 -2 Let E= 0 Find 2E. -3 5

A: Given,  E=-4-204-35

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

A:

Q: Show that E [(X-µ)^n]=0 for ∀n, with X~N(µ, σ²) and n≥3 being odd numbers.

A: We need to show; E[(X-μ)n]=0 for ∀n and n≥3 being odd numberswhere;X~Normal(μ,σ2) That is, we need…

Q: Ex let x be with pmf 1=,2,3, 16 O find c P(X)2)

A: We want to find the value of c and P(X≥2) and P(X2=9)= ?

Q: Find x for which det(A)=0 7-x -2 A = 1- x 0. 5- x The sum of the answers is....

A: See the detailed solution below.

Q: Part 4 and 5

A: Part 4. Consider the left-hand side of the equation,

Q: 2- The value of s such that P, (1) = 0.6 and 4 f(x) 1 2 1.5 None of the above options

A:

Q: 3 6. Let A= 0 x+1 1 x -8 x-1 For what values of x does A-¹ exist?

A:

Q: s+1 If F(s) = (s-3) then

A: Given: Fs=s+1ss-3

Q: (b) Pr[X > 0.6n] < 0.85. Let X be the number of HEADS after n fair coin tosses. Show that

A:

Q: 5n2 For E>0, there is a corresponding N such that -4/0 N. 4 +3 Then the value of L will be

A: Given function is , f(n)=5n24n+3

Q: Let X~N(3,0²). Suppose that P(3<X<6)=0.4 · find P(X<0) ?

A: Given: X~N3, σ2 and P3&lt;X&lt;6=0.4.

Q: 3. Suppose that the pmf of X is x-1 1. p(x) ,t = 1,2, 3, . 3 3 Find the mgf of X.

A:

Q: B A Proved (K²_K²'²') (1-²²k²a) (K+K) ² - (K-K) ² 21P9 A(KIK)- BLK-K') = F (K+K ² ) e A UKK KK 9 e…

A: Given: BA=k2-k'21-e2ik'ak+k'2-k-k'2e2ik'aAnd,Ak+k'-Bk-k'=Fk+k'eik-k'a We have to prove that:…

Q: Find all values of x for which ∑ (n=0 to ∞) 1/(1+x)^n equals 4

A:

Q: Let f (x) = -2r, de fined on -1, 1], then L (P ) = 2 (n– 1) 2- 4 (n+1) 4 (n – 1) 4 (п-1) 2n2

A: We need to find the lower Riemann sum

Q: 11. Find all values of t for which t-2 1 - 2 2 (a) 0; 3 1-3

A:

Q: 2+ x²- 2x Given g(x)= and with po= 0.5 generate p3. 3.

A: In the given question, concept of Newton's Iteration is applied. Newton's Iteration The…

Q: (27) Let X = P(2) and E(-x) = E(5 – 5x) find 2.

A: Given: A random variable X follows Poisson distribution Mathematically, X~Poi(λ) The probability…

Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

A:

Q: 5. Find the general solutions to the nonhomogencous, lincar difference cquations. (a) x,12 + X141 –…

A:

Q: 2+x²- 2x Given g(x)= and with po= 0.5 generate p1. 3.

A:

Q: 6. Suppose X -U(1.5).which is true?( ) b-a (A) Pla s X sb} = 3 (8) P{3 < X < 6} =- 4 (C) P{0< X < 4}…

A: Given that : X ~ U ( 1 , 5 )  By using uniform distribution we solve this problem.   Note :…

Q: 7. (12) Show that the hypotheses of the Mean Value theorem are satisfied and find all values…

A: 1. For the testing of the hypothesis of mean value theorem we need to know whether the function f(x)…

Q: Let f(n) = 2n – n? + 10n – 7. Show that f(n) is O(n³) using specific values of C and ng-

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.