Answer:
a) Computing the expected value E(XY) gives 1/4
b) The probability density function fZ(z) of Z = XY is calculated in the attached picture.
c) Computing E(Z) gives 1/4
Step-by-step explanation:
Comparing the computation of E(Z) using the answer to b), it shows that the values are equal.
Answer:
One of the problems humans have made is a large amount of pollution.
And so some of the ways we can fix this is;
1- Using electric cars.
2- Using reusable packaging.
3- For the final one you could use stuff that easily and quickly to break down naturally materials.
Step-by-step explanation:
Test 1 = 35÷50 = .7
.7 x 100 = 70
70%
Test 2 = 27÷40 = .675
.675 × 100 = 67.5
67.5%
Test 3 = 48÷60 = 0.8
0.8 x 100 = 80
80%
Test 4 = 75÷100 = 0.75
0.75 x 100 = 75
75%
So the order from least to greatest would be:
Test 2 - 67.5%
Test 1 - 70%
Test 4 - 75%
Test 3 - 80%
Step-by-step explanation:
In this problem, we need to arrange 150 chairs in rows for a school play. You want each row to have the same number of chairs.
We can find the prime factorization of 150 as follows :
150 = 2, 3, 5, 5
150 is not a perfect square. 144 is a perfect square and 12² = 144. So, there are 12 possible arrangements.
Given that
log (x+y)/5 =( 1/2) {log x+logy}
We know that
log a+ log b = log ab
⇛log (x+y)/5 =( 1/2) log(xy)
We know that log a^m = m log a
⇛log (x+y)/5 = log (xy)^1/2
⇛log (x+y)/5 = log√(xy)
⇛(x+y)/5 = √(xy)
On squaring both sides then
⇛{ (x+y)/5}^2 = {√(xy)}^2
⇛(x+y)^2/5^2 = xy
⇛(x^2+y^2+2xy)/25 = xy
⇛x^2+y^2+2xy = 25xy
⇛x^2+y^2 = 25xy-2xy
⇛x^2+y^2 = 23xy
⇛( x^2+y^2)/xy = 23
⇛(x^2/xy) +(y^2/xy) = 23
⇛{(x×x)/xy} +{(y×y)/xy} = 23
⇛(x/y)+(y/x) = 23
Therefore, (x/y)+(y/x) = 23
Hence, the value of (x/y)+(y/x) is 23.
