4.9) Let p(k) = P(X = k) = c2 k for k = 1, 2, 3, and p(k) = 0 otherwise. Find the value of c that makes p into a PMF.

Q: 12. Define def M e-$dWg• s=0 For each t > 0, compute (a) E[M¡]. (b) E[M?]

A: Given  Mt=∫s=0te-s dWs      , where W is a Brownian motion.

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

A:

Q: 4.3.a Use Theorem 9.4 to show that Y is sufficient for p 4.3.b Find the MVUE for p

A:

Q: O8+ Cataulali (he volume v dune of paallelpipad detemined by The veilois 3i+2K +3k. う

A: To find the volume of a parallelepiped that is determined by the below vectors. a=i−jb=3i+2kc=−7j+3k…

Q: Source d.f SS MSS Between groups 2403.5 Within groups 942 205.1 Total 193204.2 2403.5 Cannot find

A: Given: df=942MSS=205.1  We know that the formula of MSS is: MSS=SSwithindf We need to find SSwithin.

Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

A:

Q: In a test of Ho:p=0.4 against H: p 0.4, a sample of sizc 100 produces Z 31•28 for the value of the…

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will…

Q: Show that cl S = SU(Bd S) %3D

A: LetS⊆R, claim: closure(S)=S∪Bd S =S ∪ S' by definition bd(S) ={ x∈ℝ/x∉S° & x∉(ℝ-S)°} let  x∈S∪S'…

Q: Show theit the fenias +- (AtI)(28+1) (P+1)(2p41)(38+1) (uhese a>0, B>0) conveages if B>a amd…

A: Ratio test If we have series ∑ann=1∞ Then we will find the limit l = limn→∞an+1an If l<1 , then…

Q: Let X1,..., X, be independent such that X;|p ~ Bernoulli(p) with pE (0,1), and p~ Uniform(0, 1).…

A: c) Given that X1,X2,.....,Xn be independent such that Xi|p~Bernoulli (p). f(Xi|p)=pxi(1-p)1-xi…

Q: 1. Compute P(8), and find the exact values of the six circular functions given that e =- 135°. %3D

A:

Q: What is the value of k such that P(z>k)=0.0630? Previous

A:

Q: .3 T Evaluate In In e²+j²4

A:

Q: 4. Find the cubic spline g(x) for the given data with the ko = 0 and k3 = -12 as given. Xj fi 1 1 9.…

A: Use the following formulae, to find the coefficients of individual splines and the cubic spline…

Q: Consider the econometric model y = Bo + B1x +u and the OLS estimator B, for B1. We know that: O…

A:

Q: Q1. Compute xdx x'+10 using trapezoidal and Simpson's 1/3 rules with the number of points 3 and 5.

A: The given integral is, I=∫01xdxx3+10 Dividing the interval (0,1)  into 2 intervals (for 3 points)…

Q: The critical value for t for n = 9 for a one tail %3D test at a = 5% LOS is t table link:…

A:

Q: 3.5 30 21 Not drawn to scale. O SAS- Theorem O SA- Postulate O SSS- Theorem O AA- Theorem

A: There are 2 theorems for similiar triangles. SSS and AA theorem

Q: Suppose RV X has the following PMF: p(0)=0.2, p(1)=0.5, p(2)=0.3. Find E[X], E[X^2], E[X]^2.

A:

Q: Let SINGLEDFA = { | M is a DFA and for all s e L(M),|s| = 1}. Show that SINGLEDFA is decidable.

A: Detailed explanation mentioned below.

Q: The critical number(s) of f(r) = (x+ 1)/3 is (are)

A: Given,        The critical numbers of fx=x+113

Q: 2. Suppose the PDF of X is given by fx(x) = 5e-5x(o)(x). Find its CDF.

A: Solution

Q: 2. Let P: C(0, 1]C(0, 1] be given by Pp "- e. Compute dP(x). Be sure to justify your calculations.

A: Given: The given function is  P:C20,1→0,1 given by pφ=φ''-eφ

Q: 1. Find the interval(s) wheref(x) = xe6* is concave down, if such an interval exists.

A:

Q: use the beta function to compute P(3<Y≤5).

A:

Q: Σ (X) E(Y), E(XY ) , Coν ( X, Y) , σχ, σχ and ρxΥ.

A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted...…

Q: 1. By using the following data compute the Karl Pearson's coeficient of corelation. EX=250, EXT =30,…

A:

Q: /et A 3 8 カー (-45 Show That LA+B S ZA+B) 3-5 = At B

A: Transpose of a Matrix is defined as “A Matrix which is formed by turning all the rows of a given…

Q: 3. Consider the test of Ho: of = 03 against H1: of < o3. Estimate the p-value for the following fo-…

A: Given: Hypothesis is H0:σ12=σ22     Vs     H1:σ12&lt;σ22f0=0.27n1=10n2=8

Q: Is 1z = 1 for all z ∈ C?

A:

Q: A research center claims that at least 23% of adults in a certain country think that their taxes…

A: The random variable X follows normal distribution. We have to test whether at least 23% of adults in…

Q: 2. Let X~N(u, o2). Show that the MGF of X is etHtc²a².

A:

Q: Show that E(SSE) = (n - k-1), as in Theorem 7.3f, using the following approach. Show that SSE = y'y…

A: Please find the explanation below. Thank you

Q: Note that the exact ( analytical) solution was given in the tables. Yeuler |&] (%) t Ytrue 0.0 0.05…

A:

Q: Q1. Compute xdx x' +10 using trapezoidal and Simpson's 1/3 rules with the number of points 3 and 5.

A: we have  I=∫01x dxx3+10dx  n=3h=b-an=1-03=13…

Q: Given the normally distributed r.v. X with μ=25 and P(X > 10) = 0.9332, then σequals

A:

Q: b) Show, with the help of the Intermediate Value Theorem (IVT), that the average weight of seelans…

A:

Q: In order to obtain a good linear approximation for In (7.4) what would a particularly useful nearby…

A:

Q: 2. Let P:C0, 1] → C|0, 1] be given by Pp = " – e°. Compute dP(y). Be sure to justify your…

A: We have Pφ=φ''-eφ We need to find dPφ If we have  y=fx⇒dydx=f'x⇒dy=f'x dx Similarly, we find dPφ for…

Q: 1. A bowl contains 10 red and 10 yellow balls, how many balls must be selected to ensure 5 yellow…

A: To solve this type of questions we consider the worst case that is  after taking all red balls we…

Q: (3) Let A be m x n (not need to be square). What is the sum of the diagonal elements of ATA in terms…

A: (3) Given that Abe m×n matrix (not need to be square matrix). We have determine the sum of the…

Q: that H(m m). Show

A: Given function is: Hm=3m-2 We have to find the inverse function H-1m. Let Hm=y Then we get,…

Q: 03) find the ax en the sl abetwed wol y=J2-X, and y= 0

A:

Q: Estimate the value of f2 (1 – x-4x + 2x) da using 4- segment Simpson's 1/3 Rule. O 1144.5 O 2146.7 O…

A:

Q: 4. Write down the formula of the following rules for n = 12. %3D (a) Trapezoidal Rule (b) Simpson's…

A: Solution:

Q: 2. Give the condition which ensure that |ez| < 1 where z in C.

A:

Q: Suppose / (s) - (÷)*" valuate: Js(x) dr +C 3- In (5)

A: Given      f(x) = 1512-3x

Q: To test this null hypothesis, we compute t using a special case of the formula. state the formula?

A: In this case, we need to write the test statistic formula for testing the null hypothesis.