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Firdavs [7]
2 years ago
10

Find the following integrals

Mathematics
2 answers:
Hunter-Best [27]2 years ago
8 0

\large{\underline{\underline{\pmb{\sf{\color{yellow}{Answer:}}}}}}

\sf x -  \frac{4}{x}   + C

Step-by-step explanation:

\sf  \longmapsto \int  \frac{ {x}^{2} + 4 }{ {x}^{2} }dx  \\  \\  \\  \sf  \longmapsto  \int  \frac{ {x}^{2} }{ {x}^{2} } dx +  \int  \frac{4}{ {x}^{2} } dx \\  \\  \\  \sf  \longmapsto  \int 1dx + 4 \int  \frac{1}{ {x}^{2} } dx \\  \\  \\  \sf \longmapsto x + 4( \frac{{x}^{ -2 + 1}}{  -2 + 1} ) + C \\  \\  \\  \boxed{  \longmapsto x -  \frac{4}{x}   + C}

irina1246 [14]2 years ago
7 0

Answer:

x - 4/x

Step-by-step explanation:

Re write as      1 + 4 x^-2

  then you can see the integral is    x -4x^-1

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Answer:

Step-by-step explanation:

Probability distribution of this type is a vicariate distribution because it specifies two random variable X and Y. We represent the probability X takes x and Y takes y by

f(x,y) = P((X=x,Y=y) ,

and given that the random variables are independent the joint pmf isbgiven by:

f(x,y) = fX(x) .fY(y) and this gives the table (see attachment)

(b) the required probability is given by considering X=0,1 and Y =0,1

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= [0.1 +0.2 ] × [0.1 + 0.3]

= 0.3 × 0.4

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Now we find

fX(x) = sum{[f(x.y)]} for y =0, 1 and similarly for fY(y)= sum{[f(x,y)]} for x=0, 1

fX(x) = sum{[f(x,y)]}= 0.1+0.3

= 0.4

fY(y) = sum{[f(x.y)]} = 0.1 + 0.2

= 0.3

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= 0.12

Hence f(x,y) = fX(x) .fY(y), the events are independent

(c) the required event is give by: [P(X<=1, PY<=1)]

= P(X<=1) . P(Y<=1)

= [sum{[f(x.y]} over Y=0,1] × [sum{[f(x.y)]}, over X= 0, 1

= 0.4 × 0.3

= 0.12

(d) the required event is given by the idea that: either The South has no bed and the North has or the the North has no bed and the South has. Let this event be A

A =sum[(P(X = 1<= x<= 4, Y =0)] + sum[P(X =0 Y= 1 <= x <= 3)]

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A = [0.09] + [ 0.09]

A = 0.18

Pls note the sum of the vertical column X=2 is 0.3

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Answer:

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we know that

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