21 Let vi = 4 V2 = -7,V3 3 6 Does (V1, V2, V3) Sspan R?

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

A:

Q: 3 Let vį = . If u 1 vị and ul v2, then y = -1 -2 a) -9 b) -8 c) 10 d) 9 e) 7

A: We use the definition of perpendicular vectors to find the value of y.

Q: Sotve (D + 1) y = 0, t> 0, ify=yo when t= 0

A:

Q: 4R Q13:- If R = RR3 R+R2 Show that we we (R +R

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Q: 71. r(и, v) — 4ui + (Зи — v)ј + vk 0 < u < 3, 0 < v < 1

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Q: 7) Prove the following. a) (pAq) →r = (p-r)v(q-r) b) p-(q-r) = (pr)

A:

Q: Fined exy if w:f),4メーク(V=ズ」 し EXpress the anscwer in terms of U, V, fy fv soly wメyニ

A: The given question is solved in step 2.

Q: Q2: Let Z= 2 or Z=-2 and Y:bin(n, 0.38), find s.t 0.5 20.99. n

A: If  Y~Binom(n,p) Then  Z= (Y-np)/(✓npq) follows N(0,1) So using this we can find 'n' where  Z= 2…

Q: Let V = xi+ 2yi + Ozk, then [v-V =

A: ∇ is an operator and ∇=∂∂xi+∂∂yj+∂∂zk

Q: Solve the system.

A: 2x + 3y = -24x - 5y = 1u =1x  &amp;  v=1y

Q: If z = (1+ iv3)' 100 then find the value of Re(z)/Im(z). a. V3 b. 1/V3 с. 2//3 d. -V3

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Q: If I (F14)- s²+1 SO is given by? a) V(s? + 1)³

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Q: Q4 Determine i) S Inßx x²dx Sax+8 ii) çdx x²+4x4B

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Q: If z1 = 1+ jb , Z2 = re¬1² , z/z2 = -10 , determine all possible values of b and r %3D

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Q: Q. 5. Show that "-C, 1+"C, =" C, . n-1

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Q: 7x? x lif -<x< TY½ fow if -<x<T% if 计 T6exesy X< 37 3.

A:

Q: n = 29, x = 2,331, x2 = 191,077, y = 2,128, y2 = 161,876, xy = 174,226 Ξ ху — η (Σxy ) -(Σx ) (Σy)…

A: Given Information: n=29∑ix=2331∑ix2=191,077∑iy=2,128∑iy2=161,876∑ixy=174,226 Correlation coefficient…

Q: 4. proj, u 5. u x v

A: This question is related to vectors.

Q: 2. R. 12 Similar Not Similar or 16 24 18 Why? 12 9 U Triangle similarity statement:

A:

Q: Q2: Suppose A = (0,2,4,6,8), B (1,3,5,7) and C (2,8,4). Find 1) AUB %3D 2) Ance 3) BnC 4) C\B

A: Given, A={0,2,4,6,8}, B={1,3,5,7} and C={2,8,4} To find, 1) A∪B 2) A∩Cc 3) B∪C 4) C\B

Q: u = 3, o2 = 9, P(-6 < X<12) a. Determine P(u – ko < X<u+ ko) 1 - 1/k?

A: According to the Chebyshev's theorem, 1-(1/k²) of the observation fall within k standard deviation…

Q: t the three numbers be x, y, and z. Then x + y + z = 370 3 is can be rewritten as z = 370 V 370 - x…

A: Introduction: The partial derivative is used in vector calculus and differential geometry. In…

Q: |=5| (t - T)e2Tsin2T.dT 52(s² – 45 + 5), Select one: True False

A: We will check whether the given statement is true or false using convolution theorem.

Q: Find (3u − v) ∙ (u − 3v) when u ∙ u = 8, u ∙ v = 7, and v ∙ v = 6.

A: Given, u ∙ u = 8 u ∙ v = 7  v ∙ v = 6 To find:   (3u − v) ∙ (u − 3v)

Q: Q7. V(x, y) = x³ + y³ and x = 2t +r,y = 2t – r , what av? is ? ar

A:

Q: S(r, y) = S2, 0<r<y< 1, 10, elsewhere. Determine if X and Y are independent.

A: We have to check whether , X and Y are independent First we will find out the marginal probability…

Q: od and y fxom the follawing f inor B3 A - 1300 12

A: We have to find the value of angle x.

Q: value ne followin9 pro lems: i x, 11 2 4 3 5 48 59 6 11 7 14 8 17 9 18 10 20 1) 10 2) 3) 4) X = [4…

A: Solution: n= 10 observation: In the given example we need to find the summation values in the given…

Q: use determîne the ratio test to if it conver g en ce is dikergence to 3.

A: We have to find

Q: *:س 6 where The value of she vgiá dà r = |7| Cya g(r) = ! , = xi + yj + zk let And

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Q: 3. Let R= {(x, y) : x² + y² 0, y > 0}. Evaluate // Vz? + y² dA x2 +y? dA R

A: using polar coordinates x=rcos(θ)y=rsin(θ)x2+y2=r2,dA=r drdθ

Q: Q2: Let Z= 2 or Z=-2 and Y: bin(n, 0.38), find s.t 0.5 20.99.

A: If Y~Binom(n,p)  Then  Z= (Y-np)/(✓npq) follow normal distribution with parameters 0 and 1. Here…

Q: Q2: Suppose A = (0,2,4,6,8), B = (1,3,5,7) and C= (2,8,4). Find 1) AUB %3D 2) Ance 3) Bnc 4) C\B

A: Given A = 0 , 2 , 4 , 6 , 8B = {1 , 3 , 5 , 7}C = {2 , 8 , 4} then (1) A∪B = {x : x∈A or x∈B}= {0 ,…

Q: r = 1, ..., n – 1 + r r

A: From the given that,

Q: N Let y (0) X ~ Bin 0.3 {0.4

A: From the given information, X follows Binomial distribution n,Θ. PX|Θ=nxΘx1-Θn-x yΘ=0.3, Θ=Θ1,Θ20.4,…

Q: Ex Find lull, , u.v, and d(4,v). U = (-1,1) , v= (7, 9) O d(u, v)

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Q: P[N;(1) = k/{N¡(1) + N2(t) = n}] = nC p q"-k, where and q = P = 21 + 12 21 + 12

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Q: Q2. Let S(x) = (x+2), and g(x)= (x+) gof and fog find

A: From the given data:

Q: Assume that u- v = 7, ||u|| = 3, and ||v|| = 3. What is the value of 5u- (9u – 7v)?

A: Given, u.v = 7  u = 3    and   v = 3   We have to find the value of 5u.(9u-7v)

Q: For u =(5,-5) and v = (-3, 2) find u. v. u v = 2.9 u•v=

A:

Q: xz, + 2yzy = 0, for r > 0, y > 0 yzz – 4xz, = 2ry, for all (r, y) #2, – ryzy = z, for all (r, y)

A: (A) Given the PDE xzx+2yzy=0 We will use the characteristic method to find the solution.

Q: Express u = (3,-10) as a linear combination u = rv + sw, where v = (5, 1) and w = (1,−1). (Use…

A:

Q: Q4 V=R°, <uv7=U, V,+ Uz Vz+ 2U3V3 Find: ) " (4) » i) dist - ((3),E) ) dvgle in betwean i) I| andthe

A: Given vectors u and v are taken from the vector space ℝ3 and the inner product is defined as…

Q: s the folowing statement true or false? OOIGC) Vk, m, n € Z where kSm Sn O True O False

A:

Q: 27TT 3. x = y2 and x + y = 2 is revolved about y = 1. (Answer: c. u.) 2

A: We need to find the volume of the region, bounded by the curves x=y2, x+y=2 which is revolved about…

Q: (b): Find the values of V10 (Vab) (1): (a² + b²), (2): and (3): ab(a² + b²) by using fomulas if V5…

A:

Q: [2 Q2) Assume A = |1 3 11 show that (AB)' = B' A' 6. 4 and B = 13 4. 213

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.