The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation (SD) of a random variable by its mean. In this case, we are given that the random variable X follows a Poisson distribution with parameter m, and the CV of X is 50.

To find the probability that X assumes only non-zero values, we first need to understand the properties of the Poisson distribution. The Poisson distribution is a discrete probability distribution that describes the number of events occurring within a fixed interval of time or space. It is often used to model rare events that occur independently of each other.

Poisson distribution has only positive integer values (0, 1, 2, ...) as possible outcomes, but it is still possible for the distribution to assign a probability of zero to the value zero. Therefore, we need to determine the probability that X takes on non-zero values, which is equivalent to finding 1 minus the probability that X equals zero.

To calculate this probability, we can use the probability mass function (PMF) of the Poisson distribution. The PMF of a Poisson random variable X with parameter m is given by:

P(X = k) = (e^(-m) * m^k) / k!

where e is the base of the natural logarithm (approximately 2.71828).

Now we can calculate the probability that X equals zero:

P(X = 0) = (e^(-m) * m^0) / 0! = e^(-m)

To find the probability that X assumes only non-zero values, we subtract this probability from 1:

P(X ≠ 0) = 1 - P(X = 0) = 1 - e^(-m)

Since the coefficient of variation (CV) is equal to the standard deviation divided by the mean, we can express the standard deviation (σ) in terms of the mean (m) and CV as:

CV = σ / m

σ = CV * m

Substituting this into the expression for the probability that X assumes only non-zero values:

P(X ≠ 0) = 1 - e^(-(CV * m))

This equation gives the probability that X takes on non-zero values for a given mean (m) and coefficient of variation (CV).

In conclusion, to find the probability that X assumes only non-zero values when X follows a Poisson distribution with parameter m and a coefficient of variation of 50, we can use the equation:

P(X ≠ 0) = 1 - e^(-(50 * m))

Note: The above answer is given as a guide and should be reviewed and verified by consulting the relevant textbooks or educational resources.