DiscreteDistributions

Question1 (Determine the mean, variance, and standard deviation of a discretedistribution)

Adiscrete distribution exists where the observable statisticalproperties have values that are pre-defined. The possibleobservation, in this case, is limited compared to the continuousdistribution. The computation of the measures of central tendency andthose of dispersion can be computed efficiently. Therefore, it isimportant to determine the mean, variance, and standard deviationconcerning the discrete distribution.

Themean of a discrete distribution is sometimes referred to as theexpected value. When the process repeats itself for some time, theaverage of the outcomes can be computed to give the mean of thevalues. The formulae used to calculate the mean is µ = E(x) =∑[x*P(x)]. In this formula, E(x) is the mean to be calculated andP(x) gives the probability of the specified result. To find the mean,the individual figures of random variables x is multiplied by itscorresponding probability. The resulting figure is then summed up(Harshbarger, 2013).

Variancehelps find out the extent to which the random numbers diverge fromthe mean. Once the expected value is calculated, the variance can aswell be found out. In any discrete distribution, the variance isgiven by the formula

Variance(x) = σ^{2}=∑[(x- µ) ^{2}*P(x)]. Just like in case of the mean, x stands for the outcome, andP(x) is its probability. Finally, µ is the mean. To make thecomputation simpler, the deviation is calculated using (x- µ) afterwhich it is squared. Finally, the figure found is multiplied by theprobability. The total of all the values is the variance.

Oncethe value of the variance is known, then it is easier to find thestandard deviation. Usually, the standard deviation is detonated byσ, unlike the variance which presented by σ^{2}.This implies that finding the square root of the variance gives thestandard deviation. Therefore, σ =√Variance(x).

Question2 (Differentiate between a discrete distribution and a continuousdistribution give real example)

Thereexists a clear difference between the discrete and continuousdistribution. The dissimilarity occurs because of the definiteprobabilities of the variables. When there are two specified values,and the variable takes any of them, then it is a continuous variable.Otherwise it will be a discrete variable. Similarly, the continuousdistribution is never expressed in tabular form and thus an equationor formula is used to describe it.

Anexample of a discrete distribution is the tossing of a coin. Supposethe coin is flipped once, the outcome can be either a head or tail.The number of heads can either zero or infinity depending on thenumber of tosses made. Therefore, the number is an integer betweenzero and infinity. There is no way the number can be 1.5. On theother hand, continuous variable is applied in real life examples. Forinstance, a logistic company can estimate that all the vehicles totransport its data must weigh between two and three tons. This is anillustration of a continuous distribution since the lorries to beused by this firm can have any weight between two and three tones.

Indiscrete distribution, the probability is related to the variables indifferent ways. It is critical to understand the connection betweenthe two to minimize the complications that can arise in solvingrelated questions. In statistics, it is usual to come across theterms discrete and continuous distributions. They are very differentfrom one another both in definition and application when it comes toreal life situations.

Reference

Harshbarger,R. J. (2013). *MathematicalApplications for the Management, Life, and Social Science. *Boston,M: Brooks/Cole, Cengage Learning.