Given:
X ~ P(m) (X follows a Poisson distribution with parameter m)
Coefficient of variation = 50%

Definition:
The coefficient of variation (CV) is a measure of relative variability and is calculated as the standard deviation divided by the mean, expressed as a percentage.

Formula:
CV = (standard deviation / mean) * 100

Approach:
To find the probability that X would assume only non-zero values, we need to find the probability of X being greater than zero. Since X follows a Poisson distribution, we can use the formula for the probability mass function (PMF) of the Poisson distribution to calculate this probability.

Solution:

Step 1: Find the mean (m) and standard deviation (σ) of X
- We know that CV = (σ / m) * 100
- Rearranging the formula, we get σ = (CV / 100) * m
- Since X follows a Poisson distribution, the mean (m) and standard deviation (σ) of X are both equal to m.

Step 2: Calculate the probability of X being greater than zero
- The probability mass function (PMF) of the Poisson distribution is given by P(X=k) = (e^(-m) * m^k) / k!
- To find the probability of X being greater than zero, we need to calculate P(X>0) = 1 - P(X=0)
- P(X=0) = (e^(-m) * m^0) / 0! = e^(-m)
- P(X>0) = 1 - e^(-m)

Step 3: Substitute the value of m into the equation for P(X>0)
- From step 1, we know that σ = (CV / 100) * m
- Rearranging the formula, we get m = (100 / CV) * σ
- Substituting the value of m into P(X>0), we get P(X>0) = 1 - e^(-(100 / CV) * σ)

Step 4: Calculate the probability using the given coefficient of variation
- CV = 50% = 0.5
- Substituting CV = 0.5 into the equation for P(X>0), we get P(X>0) = 1 - e^(-(100 / 0.5) * σ) = 1 - e^(-200 * σ)

Step 5: Find the probability that X assumes only non-zero values
- P(X assumes only non-zero values) = P(X>0) = 1 - e^(-200 * σ)

Step 6: Substitute the value of σ
- From step 1, we know that σ = m
- Substituting σ = m into the equation for P(X assumes only non-zero values), we get P(X>0) = 1 - e^(-200 * m)

Step 7: Find the probability using the given distribution
- Since X follows a Poisson distribution, the parameter m is given in the problem.
- Substitute the value of m into the equation for P(X assumes only non-zero values), we get P(X>0) = 1 - e^(-200 * m)

Step