Answer:
Step-by-step explanation:
Given that:
X(t) = be the number of customers that have arrived up to time t.
... = the successive arrival times of the customers.
(a)
Then; we can Determine the conditional mean E[W1|X(t)=2] as follows;
Now 
(b) We can Determine the conditional mean E[W3|X(t)=5] as follows;
Now; 
(c) Determine the conditional probability density function for W2, given that X(t)=5.
So ; the conditional probability density function of 
given that X(t)=5 is:
They want to know the probability of landing in the blue and red section at the same time. In other words, they want to know the probability of landing in the purple section.
We'll need the area of the purple square. This square is 1.5 inches by 1.5 inches. This is because 4 - 2.5 = 1.5
So the purple square has an area of 1.5*1.5 = 2.25 square inches
Divide this over the total area of the largest square (which is 9x9) to get 2.25/81 = 0.02777... where the 7's go on forever
Round that to two decimal places. The final answer is 0.03
Side note: 2.25/81 is equivalent to the reduced fraction 1/36 (express 2.25/81 as 225/8100 and then divide both parts by the GCF 225)
<span>This question, in my opinion, is not well stated. If f(x) = √x, as the question statement seems to say, then the domain is not x<7. Rather, the domain is x≥0.
If f(x) is not the square root function, but say f(x) = √(7-x) then the domain is x≤7, and for this function then the appropriate answer is d), since the x-term inside the radical has a negative coefficient.</span>
5k^3 - 3k + 7 + <span>2k^3 - k^2 + 9
= 7k^3 - k^2 -3k + 16</span>
