Answer:
The value of
.
The value of
.
Step-by-step explanation:
Consider the provided information.
The number of hours between successive train arrivals at the station is uniformly distributed on (0, 1). Passengers arrive according to a Poisson process with rate 7 per hour.
Let X denote the number of people who get on the next train.
Part (A)
Here, X = N(T), N(t) ∼ Poisson(λt), and λ = 7
Therefore, E(N(T)|T) = λT
Now find E(X) as shown below



Hence, the value of
.
Part (B)
Now we need to find VAR[X]




Hence, the value of 
Answer:
42.9 cm^3
Step-by-step explanation:
Volume of the box= (base x width x height) = 8.5 x 5 x 5 = 212.5 cm^3
Radius of a ball = 1.5 cm
Volume of a ball = 4/3 * radius^3 * pi = 4/3 x 1.5^3 x pi = 14,137167 cm^3
Volume of the balls = 14,137167 x 12 = 169,646003 cm^3
Final answer = 212.5 - 169,646003 = 42.9 cm^3
Answer:
12.5
Step-by-step explanation:
It is equal to the slope of the line = 50/4 = 12.5