Answer:
Cov (X,Y) = 6
Step-by-step explanation:
hello,
Cov(X,Y) = E(XY) - E(X)E(Y)
we must first find E(XY), E(X), and E(Y).
since X is uniformly distributed on the interval (0,12), then E(X) = 6.
next we find the joint density f(x,y) using the formula
this is because f is uniformly distributed on the the interval (0,12)
also since the conditional probability density of Y given X=x, is uniformly distributed on the interval [0,x], then
for 0≤y≤x≤12
thus
.
hence,
also,
thus Cov(X,Y) = E(XY) - E(X)E(Y)
= 24 - (6)(3)
= 6
Answer:
85% decrease
Step-by-step explanation:
The percentage change is the change fraction multiplied by 100%.
percent change = change / original × 100%
= (3 -20)/20 × 100%
= -17/20 × 100% = -85%
A decrease from £20 to £3 is a change of -85%.
Answer:
Step-by-step explanation:
The probability that you make one shot is 70%, or 0.7.
The probability that you make 10 shots is the probability that you make 10 shots in a row. This means that you have to make the first shot AND the second shot AND the third shot and so on. The probability of two independent events both happening is P(A) * P(B), and we can apply that here. Each shot has a 0.7 chance of success, so we multiply that 10 times to get (0.7)¹⁰=0.0282475249
The probability that you make 9 shots can be represented by the following combinations, with M representing a miss and S representing a make.
MSSSSSSSSS
SMSSSSSSSS
SSMSSSSSSS
and so on. There are 10 possible combinations as there are 10 possible places where you can miss but still make 9. The probability of one of these combinations happening is
(0.3) for the miss multiplied by the probability of all the rest making it, or (0.7)⁹ = 0.3 * 0.7⁹ = 0.0121060821
Then, we multiply by 10 because there are 10 possible combinations, resulting in 0.121060821. Add this to the probability of making all 10 to get
0.0282475249 + 0.121060821 = 0.1493083459