Find Expected Number of Cakes per Person: Bernoulli to Gamma

[ackr1201]

Solve this??

There are w cakes and n people. The cakes are distributed to people randomly. Find the expected number of cakes a 'i' person can receive. The distribution is:
a) Bernoulli distribution

b) Binomial distribution

c) Poisson distribution

d) Uniform distribution

e) Exponential distribution

f) Normal distribution

g) Chi-square distribution

h) Gamma distribution

 

[micromass]

what did you try??
Is the distribution discrete or continuous??

 

[ackr1201]

@micro mass : I didn't get.. I am poor at propbabilty and statistics

It follows discrete distribution

Plz help me..

 

[micromass]

I am helping you, but I'm not just telling the answer until you tell me what you think and what you tried.

 

[blue_raver22]

To solve this problem, we can use the Bernoulli to Gamma distribution. This distribution is a mixture of the Bernoulli and Gamma distributions, and it is commonly used to model the number of successes in a sequence of independent trials. In this case, the "success" would be receiving a cake.

To find the expected number of cakes per person, we first need to calculate the probability of success in a single trial. This can be done by dividing the total number of cakes (w) by the total number of people (n). Let's call this probability p.

Next, we can use the formula for the expected value of a Gamma distribution, which is E[X] = kθ, where k is the shape parameter and θ is the scale parameter. In this case, k would be n (the number of trials) and θ would be p (the probability of success).

Therefore, the expected number of cakes per person would be n * p = w/n. This means that on average, each person would receive w/n cakes.

In conclusion, by using the Bernoulli to Gamma distribution, we can find the expected number of cakes per person in this scenario. It is important to note that this is an expected value and does not guarantee that each person will receive exactly w/n cakes, as the distribution is random.