(0. }). (c) C = {p : p is prime). (d) D = (-0, –1). (a) A = (b) B = {-1,1}.

Q: Equating the coefficients of corresponding powers of t gives 2/3(13A2 + 2) = 10A2 + 1, (2.200)…

A: 2313A2+2=10A2+1   .....(1)2935A3+10A2=10A3+2A2     ...(2) We need to solve the equations to find the…

Q: Q3:- find the erea of the shap by the order 1- SS dydx 10

A: Please refer the attached image for complete solution.

Q: Evaluate fSS, 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: we need to evaluate the triple integration. For finding the solution first we will find the limits…

Q: If you apply two steps of the Secant Method to x3 = 2x + 2 initial guesses x0 = 1 and x1 = 2, Then…

A:

Q: Juneten and be fure at lebel aut least thre f (n) : Su

A: As asked we can find the answer as below

Q: sn'x プェ Sec'x-1 from [o, of 2.

A:

Q: Sin (n+))x Conv. unif nナノ on Prablem (5) Is the senies

A: The given series is: ∑n=1∞sinn+1xn+1 The given interval is: 0,π

Q: using the false - position to doter mine the voot of the eqution fcx) = 0-7 x5- 8X* +44 x-90 x+82 X…

A: Suppose the root of the function f(x) lies in the interval xl,xu. To obtain the solution of the…

Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

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Q: 2 (ii) using Convolution theorem. (s+2)(s²+9)

A:

Q: Evaluate , 5y²dV where E is the reqion below x + 3y + 6z = 9 in the first octant.

A: Given: In the first octant, evaluate∫∫∫E5y2dV , where E is the requirement below x + 3y + 6z = 9 .

Q: - - 9. - [1.0001 x* H. Verify Let A 6 = the error %3D 1.0001 formula |r* – ô|| ||r|| < K(A)-

A: Let A=2112, b=33, x^=1.00011.0001, x*=11. Verify the error formula x*-x^x*≤KArb.

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

A:

Q: Show Sn+3 diverges by osing 6n +5 the test for divegence 1こV

A:

Q: 5- Find L-1 5² (s²+4)² by using Convolution theorem.

A:

Q: 2. Use the Root Test to determine absolutely or diverge. 4n+3\ n (a)E-1( Zn=1 Зп-5) (b) E (-In (e²…

A: As we have to use the root test , So first I have written the Root test then using them for both the…

Q: Prove that L ={(1Z*)"10" | n e N}is not regular.

A: The given language: Then, the above language can be rewritten as, To prove that L is not regular.…

Q: = x3 + x - rith starting d with the of x after the

A:

Q: The evaluation of S V1 + tan2x dx is C In(V2) +1 In(vZ+1) C In(vZ-1) O-In(vZ+1)

A:

Q: We now need to attempt to find an exact value for n such that P(r ≥ 1) = 0.99. Clearly, if the…

A: We have to fill blank of P(r ≥ 1) = 1 − P ( ___ )

Q: (i) Find the constant term in the expansion of x+-

A: You have given 3 different questions in picture, without mentioning any particular questions. We can…

Q: 03 Solve the diferential eauation ecosx-0. COSY-o by Milne s method with h-ol

A:

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: converges, then C„-)" " con COr n=0

A: We have to choose the correct answer from the given option according to the given series

Q: Find length of the cardioid r=a0³from 0 = 0 to 0 = n %3D

A: Length of the cadioid is given by below formulaLength = ∫0πaθ3dθ

Q: Proof by contrapositive that for xy EZ, if xy is even then either x or y is even.

A:

Q: 2. Rainwater accumulates in the ditch as follows: 10 centimeters of water in the 1st second, 15…

A:

Q: Fincd dy for y-sinner} er tot

A: Explanation of the solution is given below...

Q: () 2k = 3", Vn E N k k=0 k n+1 Σ 2 Vn E N, n > 1 3 k=2 į * () 主) n 3k = 4", Vn E N %3D k k=0 = 2"-1,…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 34) Ź (K²_2K) is e (n3) Ź ķ? ビ=3 Ź 2K = k=3 ntro)(2n+1), entntt) Sungs are さ。 2n3+ 3n?+n – ant- Gn…

A: We have solve the given  problem

Q: 5r² – 3)| -6,80 n=3 with Simpson's 3/8 rule. Find the approximate solution for

A: Simpson's 3/8 rule is: ∫abydx=3h8(y0+2∑ i=1n/3-1(y3i) +3(y1+y2+y4+y5+....+yn-2+yn-1)+yn)here y=f(x)…

Q: Suponga P(Z,=K) = 2 Determine la distribucioñ de Zn. Ejercicio (DistrbugER del proceso de…

A:

Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: Find lower bound for f(n) = 5n².

A: To find the lower bound for f(n) = 5n2

Q: pitcher of buttermilk initially at 25°C is to be cooled by settling in on a place where the…

A:

Q: z/(z-3)2 dz ; C: |z+3| =3 slove by residue theorem

A: The given integral is,

Q: determine the radius and convergence of E n=1 5xn/3n2

A:

Q: 4. So -dy Vy+1

A: To evaluate: ∫01yy3+1dy Substitute y3=u2⇒13y-23dy=2u du⇒13u4dy=2udu⇒dy=6u5du. As y→0⇒u→0, y→1⇒u→1…

Q: 2 Given! e- 3x =0; x6 [o; 1] a1) Use two interations 0f the Secant methoed to estimate fhe root P of…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: R(Z) = 22212 S2)ク りェ Find. (ROR)( (Sos) (2)

A: Given function                                                 Rz=2z2+2 and Sz=3z…

Q: Q4 Legendra polmomial Pe (X) =2 + (3x+1) than Prove that (2u+1) Puck) =Pmnil (X) -P(X) n-1

A:

Q: 5: A. Using convolution to find L¹ [(5+2)(s+4)

A:

Q: P(x) 1 2 5 6 IRound to fonur darimal nlarae ae neerlad 4)

A: here use binomial distribution with parameter p = 0.7 and n =6 for binomial theorem ,…

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

A: Selecting two points x and y from the interval (0,1) is identical to selecting a single point from…

Q: An investigator arrives in a crime scene where a dead body of the victim was found. He arrives at…

A:

Q: Solve for nif n Py=60(nc)

A: We know that nP4 = n!/(n-r)! nCr = n!/(r!(n-r)!)

Q: 1 A. Using convolution to find L¹ [(5+2)(s+4)].

A: Convolution Theorem : If L-1F(s)=f(t) and L-1G(s)=g(t) then L-1F(s).G(s)=∫0tf(u).g(t-u)du. (As per…

Q: 1. Using Gauss-Seidel and Jacobi Method, find the values of x1, x2 and x3 with ek < 0.001. 2x — 6х,…

A:

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!