P(C|AUB) P(AUB|C) = P(C|A) + P(C|B), where AnB = 0 = P(A|C') + P(B|C) − P(An B|C) P(Aº|B) = 1 − P(A|B)

Q: Find (a) P(X ≤ 2, Y = 1); (b) P(X > 2, Y ≤ 1)

A: a) X ≤ 2 means X=0,1,2  Using that we get: P(X ≤ 2, Y = 1)=P(X=0,Y=1)+P(X=1, Y=1)+P(X=2,…

Q: Use the elimination method to find a general solution for the given linear system, where…

A:

Q: [2x*dx (Ans. 3 2 x' +c ); (xi) J3x°dx - 3 In\x)| 3 |3x'dx (Ans. (Se* –x? +2)dx , (x + 0) (x) x' +c);…

A:

Q: S Sifoo-gool dx O d2 (f.g) = Sup {/fox) - gox|} V£₁9 € [0₂4] if d, (fig) = Find Ⓒd₁ (√x,x) @d₂…

A:

Q: Find F(s). F(s) = £{t(et + e5t)2}

A:

Q: If f(z) = (a") + and f(z +y) + f(z-y) Kf(z)f(y), then the 21 value of K.

A: Given that: *f(x)=ax+a-x2 *f(x+y)+f(x-y)=K×f(x)×f(y) Thus, the function f(x+y) is,…

Q: Let plx)= 6x f(x) f"(x)= f"(-2) = 5-3 %3D 2.

A: Recall: dxndx=nxn-1

Q: Let f(x, y, z) = x³ + 5x²yz + 3xz+ 3, v = Then: D, f(a) = 201 0 -2 and a = -5 2 -5

A: Given that f(x, y, z) =x3 +5x2 y z +3xz+3 The directional derivative is a concept from multivariable…

Q: (a) div (g) = Ag clas div (fDg) = \f • Dg + f Ag Show that

A:

Q: Q: S (MATH. DЕРТ) A3 (STAGE 3) Al (STAGE 1) A2 (STAGE 2) A4 (STAGE 4) No. of student No. of student…

A: From table it is clear that

Q: f(x, y) = x²/(1 + y²) (a) f(-5, 0) (b) f(14, 1) (-) (c) | (d) f(-8, y)

A: Put value of x and y in given equation.

Q: If FGx) = -2x+s firid f(z)

A: Given: if f(x)=-2x+54To find: f(1)

Q: Q2. P(A) = 0.42, P(B|A) = 0.66 and P(B|A’) = 0.25. Find the following – P(A’), P(B’|A), P(B’|A’),…

A: We have given information, P(A)=0.42 PB|A=0.66 P(B|A')=0.25

Q: Find general solution of U" + U = 0.

A: Given differentiation equation is U''+U=0. We have to find the general solution of the given…

Q: (5, 2)

A:

Q: x(n) = a¹sin (w¸n) u(n)

A:

Q: Compute f 3 2 x-5x+6 dx.

A:

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Q/ Let X be the r.v such that E(X) = 2, E(X²)= 2a , E((2+aX)²) = 2a3 Find the value of a. %3D %3D

A: Let X be the random variable such that, E(X)=2, E(X2)=2a, E((2+aX)2)=2a3

Q: dx Use a trig substitution to evaluate x³ Vx² x > 1. 1 6. -

A:

Q: How do I find A’ , Is It B,D and F ?

A: Given U = {a,b,c,d,e,f,g}A = {a,c,e,g}B = {a,b,c,d}A' is nothing but compliment of the set A which…

Q: ▼ × (-y + x, x² + 3zy, zxy³) =? O (3y - 3zx², zx³, −2+x) O(-3y + 3xy²z, -y³z, 1+ 2x) ○ (2y + x²z,…

A:

Q: Compute f 2x-1 (x-5) (3x+1)(4x-7) -dx.

A:

Q: Differentiate V(x-2)3 y = , (x + 1)²(2x – 1)

A: We have to find derivative

Q: r(2,4) Sa (2y+x) dx +(3x– y)dy} along the straight line x-2t and Evaluate J(0,3) y=P+3.

A:

Q: he value of a.

A: Let X be the R.V  Given E(X)=2, E(X2)=2a, E((2+aX)2)=2a3

Q: If f(a) = x+ Sx ,find (a) fezf"(20), C6) (f")'(20) 3.

A:

Q: The number of visits to a website is known to have a Poisson distribution with a mean of 7 visits…

A: Given,The average no.of visits per minute is 7.