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Flura [38]
3 years ago
10

PLEASE ANSWER ASAP

Mathematics
1 answer:
Natali [406]3 years ago
6 0
Maybe Option 2? Not really sure just trying to help
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Let Y1 and Y2 have the joint probability density function given by:
Ann [662]

Answer:

a) k=6

b) P(Y1 ≤ 3/4, Y2 ≥ 1/2) =  9/16

Step-by-step explanation:

a) if

f (y1, y2) = k(1 − y2), 0 ≤ y1 ≤ y2 ≤ 1,  0, elsewhere

for f to be a probability density function , has to comply with the requirement that the sum of the probability of all the posible states is 1 , then

P(all possible values) = ∫∫f (y1, y2) dy1*dy2 = 1

then integrated between

y1 ≤ y2 ≤ 1 and 0 ≤ y1 ≤ 1

∫∫f (y1, y2) dy1*dy2 =  ∫∫k(1 − y2) dy1*dy2 = k  ∫ [(1-1²/2)- (y1-y1²/2)] dy1 = k  ∫ (1/2-y1+y1²/2) dy1) = k[ (1/2* 1 - 1²/2 +1/2*1³/3)-  (1/2* 0 - 0²/2 +1/2*0³/3)] = k*(1/6)

then

k/6 = 1 → k=6

b)

P(Y1 ≤ 3/4, Y2 ≥ 1/2) = P (0 ≤Y1 ≤ 3/4, 1/2 ≤Y2 ≤ 1) = p

then

p = ∫∫f (y1, y2) dy1*dy2 = 6*∫∫(1 − y2) dy1*dy2 = 6*∫(1 − y2) *dy2 ∫dy1 =

6*[(1-1²/2)-((1/2) - (1/2)²/2)]*[3/4-0] = 6*(1/8)*(3/4)=  9/16

therefore

P(Y1 ≤ 3/4, Y2 ≥ 1/2) =  9/16

8 0
3 years ago
|x-5|=7 What is x? PLZ help I'll give Brainliest.
mixer [17]

Answer:

x=12

Step-by-step explanation:

7+5=12

brainliest?

6 0
3 years ago
HELP
aleksandrvk [35]

Answer:

3,1

Step-by-step explanation:

(3+6)= 9

times 1 would also be 9.

4 0
3 years ago
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What is 0.6 x 2.2 = ?
Mariulka [41]
Your answer is 1.32                  
4 0
3 years ago
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Answer<br> please <br> for all five
labwork [276]

Answer:

fna-yzqk-yus

j.o.i.n gi.r.ls to see my d.ic.k and c.u.m.mi.ng

8 0
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