# a continuous random variable x assumes an (infinitely) uncountable number of distinct values: Statistics: Discrete and Continuous Random Variables

48. A consumer who is risk averse is best characterized as . 37. An analyst has constructed the following probability distribution for firm X’s predicted return for the upcoming year. 30.

E.) Cannot be determined. Special case of normal distribution will a mean equal to zero and a standard deviation equal to one. B. A consumer who demands a positive expected gain as compensation for taking risk. 14.

Refer to Exhibit 5-11. What is the probability that at least two of the customers redeem the coupon? What is the probability that no more than one of the customers redeems the coupon? What is the probability that three of the customers redeem the coupon?

What is the probability that none of them has a degree in economics? Refer to Exhibit 5-4. The standard deviation is.

## Statistics

The entire area under the curve equals 1.0. The continuous normal distribution can describe the distribution of weight of adult males. For example, you can calculate the probability that a man weighs between 160 and 170 pounds. Mutually exclusive and collectively exhaustive events contain all outcomes of a sample space, and they do not share any common outcomes.

It can of course also be a mixture of both (or to make things even weirded be ‘singular’, see e.g. the Cantor-distribution). Such singular distributions are not common in statistics , but are ubiquitous in other areas. See singular distributions applications and instances.

• What is the expected number of cars sold by the salesman during a week?
• The random variable assumes a countable number of distinct values.
• Given that the player is drawing from a full poker deck of 52 cards, find the probability that this player will draw two aces from the deck.
• Neither is it discrete, it is singular.

The complement of an event A, denoted by AC, within the sample space S, is the event consisting of all outcomes of A that are not in S. Events are exhaustive if they do not share common outcomes of a sample space. The expected value of a random variable X can be referred to as the population mean. The standard deviation is the positive square root of the variance. In general whether a distribution is discrete or continuous depends on the distribution function.

## A Discrete Random Variable X May Assume an (Infinitely) Uncountable

A Poisson random variable counts the number of successes over a given interval of time or space. The mean and variance of the standard normal distribution are ____________, respectively. The variance of the standard normal distribution is equal to ________.

A case in point is dynamics, with the famous Smale’s horseshoe, where a continuous random variable x assumes an (infinitely) uncountable number of distinct valuess supported on dynamical Cantor sets abound. Each different choice of specific numerical values for the pair $$\mu$$ and $$\sigma$$ gives a different bell curve. The value of $$\mu$$ determines the location of the curve, as shown in Figure $$\PageIndex$$. In each case the curve is symmetric about $$\mu$$. Find $$P(X \leq 0.2)$$, the probability that $$X$$ assumes a value less than or equal to $$0.2$$.

What is the probability that exactly one of the pit bulls in Joe’s group attacked another dog last year? Exhibit 5-10. According to a study by the Centers for Disease Control and Prevention, about 33% of U. Births are Caesarean deliveries .

## A continuous random variable x assumes an (infinitely) uncountable number of distinct values.

The mean and variance of a continuous random variable can be determined with the help of the probability density function, f. Of a continuous random variable is the counterpart to the probability mass function of a discrete random variable. For a continuous random variable, one characteristic of its probability density function f is that the area under f over all possible values of x is…. 57.

If we define the random variable X as sales, then X follows the… The probability that a normal random variable X is less than its mean is equal to… A function that assigns numerical values to the outcomes of a random experiment. A risk-averse consumer may decline a risky prospect even if it offers a positive expected value. The shaded region under the curve in this example represents the range from 160 and 170 pounds. The area of this range is 0.136; therefore, the probability that a randomly selected man weighs between 160 and 170 pounds is 13.6%.

For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed$10-off coupons. 72.

88. 87. The height of the probability density function f of the uniform distribution defined on the interval is… A continuous random variable X follows the uniform distribution with a lower limit of a and an upper limit of b. The expected value of X is calculated as ____________.

The relationship between the variance and the standard deviation is such that the standard deviation is the positive square root of the variance. Suppose you were told that the delivery time of your new washing machine is equally likely over the time period 9 am to noon. If we define the random variable X as delivery time, the X follows the.. If X is a normally distributed random variable, then…

A continuous random variable and a discrete random variable are the two types of random variables. A random variable is a variable whose value depends on all the possible outcomes of an experiment. A continuous random variable is defined over a range of values while a discrete random variable is defined at an exact value. This property implies that whether or not the endpoints of an interval are included makes no difference concerning the probability of the interval.

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If the possible https://1investing.in/ of a random variable can only be described using an interval of real numbers , then the random variable is continuous. If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population? A.) For any sample size n, the sampling distribution of the sample mean is normally distributed.