# Random variable and expected average return

Random variables working with uncertain numbers chapter outline 71 discrete random variables 156 finding the mean and standard deviation 156 72 the binomial the mean or expected value of a discrete random variable is an exact number your (and your firm's) “risk versus return” preference to deter. We note that the value we have chosen for the average gain is obtained by taking expected value definition 61 let x be a numerically-valued discrete random variable with sam- ple space ω and distribution function m(x) the expected one can also interpret this number as the expected value of a random variable to. In the mr and ms cabt raffle draw, there is one winner of p 10,000, one winner of p 5000, and five winners of p1000 one thousand tickets are sold at p10 each find the expectation if a person buys one ticket mean and variance of random variables mean of a random variable gain x 10 990 4,990. Eq (17) shows that e[x] is a probability weighted average of the possible values of x example 21 expected value of discrete random variable using the discrete distribution for the return on microsoft stock in table 11, the expected return is computed as: e[x] = (−03) о (005) + (00) о (020) + (01) о (05. Hence, often, when the average is discussed, we mean the sample average ( funny word play there) we compute the sample average on a given set of random variables (sample), that is a set of outcomes of a distribution this average may yield different properties with regards to the estimation of the.

Discrete random variable standard deviation calculation random variable mean: random variable mean discrete random variable standard deviation: random standard deviation. An introduction to the concept of the expected value of a discrete random variable i also look at the variance of a discrete random variable the formulas a. Drill problems 2 with answers problem 1: bond rating 1 a triple a rated firm has a default probability of 00002 in any given year what are the chances a triple a firm defaults in the next 25 years answer: pr(default in 25 yrs) = 1 - pr(no default in 25 years)25 = 0004988 problem 2: bond rating 2 a firm with a. Will study the conditional expected value of y given x, a concept of fundamental importance in probability as we will see, the expected value of y given x is the function of x that best approximates y in the mean square sense note that x is a general random variable, not necessarily real-valued in this section, we will.

Eg, the approximate probability that the return will be in a 1% range around the mean 10%, equals the height of the graph at 10% (which is 8) times 1% or 001, or 8 x 001 = 08 or 8% however, it only the expected value, or mean, of a random variable is the 'average' value that the random variable takes it is defined as. Well only if you have a continuous function or some special cases of discrete values if you have a discrete variable the mean most likely will not be a valid value in your discrete universe imagine you random variable is a boolean, the mean will not be a boolean most likely so it will not be the “expected” value. Is defined as the expected quadratic difference of the random variable's realizations and the expected value of the random variable: as continuous returns are additive (proofed in our article about properties of linear, discrete and continuous returns) we can use the arithmetical average as an estimation for the expected.

Be the sample space of all inputs of size n • to talk about expected (/average) running time, we must specify how we measure running time – we want to turn each input into a number (runtime) – random variables do that • we must also specify how likely each input is – we do this by specifying a probability distribution. Thus markowitz' approach is often framed in terms of the expected return of a portfolio and its standard deviation of return, with the latter serving as a measure of risk the expression erf(x)/sqrt(2)) gives the probability that a normally- distributed random variable will fall between -x and +x standard deviations of the mean.

## Random variable and expected average return

The ev of a random variable gives a measure of the center of the distribution of the variable essentially, the ev is the long-term average value of the variable because of the law of large numbers, the average value of the variable converges to the ev as the number of repetitions approaches infinity the ev is also known as.

• Be able to compute and interpret quantiles for discrete and continuous random variables random variables these summary statistics have the same meaning for continuous random variables: • the expected value µ = e(x) is a measure of location or as before, the expected value is also called the mean or average.
• Finding the mean (or expected value) of a discrete random variable so for number of outcomes in a week to generate random variables, one has to assume that on any given day, one decides to exercise or not randomly in reality, one decides based on his schedule that may vary systematically and hence difficult to be.
• The expected return (or expected gain) on a financial investment is the expected value of its return it is a measure of the center of the distribution of the random variable that is the return it is calculated by using the following formula: e [ r ] = ∑ i = 1 n r i p i {\displaystyle e[r]=\sum _{i=1}^{n}r_{i}p_{i}} e[r]=\sum _{{i=1}}.

Unlike the sample mean of a group of observations, which gives each observation equal weight, the mean of a random variable weights each outcome xi according to its probability, pi the common symbol for the mean (also known as the expected value of x) is , formally defined by the mean of a random variable provides. Expected value and sd of a binomial random variable the expected value e (x) is also called the average or mean of x, and denoted $\mu$ the standard deviation of a binomial returning to the example, since n=300 and p=20, we have e(x)= 300 (20) =600, and \$\mbox{sd}(x)= \sqrt{ 300. The mean (or expected value) of x gives the value that we would expect to observe on average in a large number of repetitions of the experiment important concept of expected value describe the expected monetary return of experiment sum of the values, weighted by their respected probabilities example (exercise 13). Calculate the portfolio variance: = 052 0012492 + 052 000462 + 2 05 05 00000561 = 000007234 therefore, the standard deviation is 000007234 1/2 = 000851 reading 9 los 9l calculate and interpret the expected value, variance, and standard deviation of a random variable and of returns on a portfolio.

Random variable and expected average return
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