Answer:

Step-by-step explanation:
Kindly refer to the image attached in the answer region for labeling of triangle.
<em>AB </em><em>= 16
</em>
<em>BC </em><em>= 19</em>
<em>AC </em><em>= 15
</em>

We have to find the <em>angles </em><em>x</em> and <em>y</em> i.e.
.
Formula for <em>cosine rule</em>:

Where
<em>a</em> is the side opposite to
,
<em>b</em> is the side opposite to
and
<em>c</em> is the side opposite to
.

Similarly, for finding the value of <em>y:</em>

Hence, the values are:

Answer:
0.1274
Step-by-step explanation:
Let X be the random variable that measures the number of children who get their own coat.
Then, the expected value of X is
E[X] = 1P(X=1) + 2P(X=2)+3P(X=3)+...+10P(X=10)
The probability that a child gets her or his coat is
P(X=1) = 1/10
To compute the probability that 2 children get their own coat, we notice that there are 10! possible permutations of coats. The two children can get their coat in only one way, the other 8 coats can be arranged in 8! different positions, so the probability that 2 children get their own coat is
P(X=2) = 8!/10! = 1/(10*9) and
2P(X=2) = 2/(10*9)
Similarly, we can see that the probability that 3 children get their own coat is
P(X=3) = 7!/10! = 1/(10*9*8) and
3P(X=3) = 3/(10*9*8*7)
and the expected value of X would be
E[X] = 1/10 + 2/(10*9) + 3/(10*9*8)+...+10/10! = 0.1274
Answer:
8 3/4 cubic or 8.75
Step-by-step explanation:
To find volume it’s
Length * width * height
Answer:
a) P ( 3 ≤X≤ 5 ) = 0.02619
b) E(X) = 1
Step-by-step explanation:
Given:
- The CDF of a random variable X = { 0 , 1 , 2 , 3 , .... } is given as:
Find:
a.Calculate the probability that 3 ≤X≤ 5
b) Find the expected value of X, E(X), using the fact that. (Hint: You will have to evaluate an infinite sum, but that will be easy to do if you notice that
Solution:
- The CDF gives the probability of (X < x) for any value of x. So to compute the P ( 3 ≤X≤ 5 ) we will set the limits.

- The Expected Value can be determined by sum to infinity of CDF:
E(X) = Σ ( 1 - F(X) )

E(X) = Limit n->∞ [1 - 1 / ( n + 2 ) ]
E(X) = 1