Final answer:
The parameter m for an exponential distribution X ~ Exp(0.75) is the decay parameter, which here is 0.75. The mean and standard deviation of this distribution are both equal to 1/0.75 or approximately 1.33.
Step-by-step explanation:
When it is stated that a distribution is given as X ~ Exp(0.75), what is being described is an exponential distribution, where the parameter m equates to the rate or decay parameter of the distribution. In this context, m is the reciprocal of the mean (µ) of the distribution. Therefore, m = 0.75 represents the rate at which the probability of an event decreases exponentially. The mean (µ) of an exponential distribution is given by µ = 1/m, and hence for this distribution, the mean would be µ = 1/0.75. It is also important to note that the standard deviation (σ) of an exponential distribution is equal to the mean. Therefore, in this case, both the mean and the standard deviation would be 4/3 or approximately 1.33.