he mean number of patients admitted per day to the emergency room of a small hospital is 2.5. If, on any given day, there are only 3 beds available for new patients, what is the probability that the hospital will not have enough beds to accommodate its newly admitted patients? P(Y > 1- (formula) (numeric result) se: y for the value of the variable ( ) for fractions ( )! for factorial e*( ) for the exponential function ote: You can earn partial credit on this problem.

If Y ~ Exponential(3), a > 0 and 6 > 0, show that P(Y > a+b|Y > a) = e-b/B.

The lifespans of light bulbs are known to follow an exponential distribution. The exponential distribution, often denoted exp(β), is characterized by a single mean parameter β. The exponential distribution has a unique property that its standard deviation is equal to its mean. Suppose you order 100 light bulbs known to each have lifespans (in years) distributed according to exp(4). What is the probability that the average lifespan of your 100 light bulbs exceeds 5 years? (Using R it possible)

14/13 = x/13

D = 10^3.14 * T^-1.78 D = Days T = Tornadoes

Suppose that the time in minutes, Y , that an insect spends on a plant is exponentiallydistributed such that Y ∼Exp( 1/3)(a) Evaluate P(Y ≤3)(b) Evaluate P(Y > 4)(c) Evaluate P(2 < Y < 6)(d) What is the mean length of time that this insect spends on a plant?