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1. Define “continuous probability distribution” and cite at least 5 types.

2. Define expected value and variance of a continuous random variable.

3. Describe normal distribution and the process of solving probability problems involving normal distribution.

4. Explain normal approximation to binomial distribution and how it is used in solving probability problems.​

Respuesta :

Continuous variables are variables such as time, pressure, height, length, temperature and weight

The responses are;

1. Continuous probability distribution is a distribution in which the values of

the random variable X is not limited to certain values, and therefore the

values are not countable

Five types of continuous random variable are;

  1. Normal distribution
  2. Student t-distribution
  3. Chi-square distribution
  4. F-distribution
  5. Chi-square distribution

Others include

  • Gamma distribution
  • Beta distribution
  • Cauchy distribution

2. The expected value of a continuous random variable, X, is defined as follows;

[tex]\displaystyle The \ expected \ value, \ E[X] = \int\limits^{\infty}_{-\infty} {x \cdot f(x)} \, dx[/tex]

3. The normal distribution the usual distribution used for variables that are

randomly generated and independent. It is a continuous probability

distribution also referred to as Gaussian distribution

The shape of the graph the normal distribution is bell shaped with the

maximum point being the average or mean value, while the standard

deviation gives the dispersion from the mean

The process of solving probability problems involving normal distributions

includes;

  • Define the value of the probability required in the following form;      p(x < a), p(x > b), p(a < x < b)

The z-score of a, (and b) is then determined as follows;

  • [tex]Z=\dfrac{a-\mu }{\sigma }[/tex], and/or [tex]Z=\dfrac{b-\mu }{\sigma }[/tex]
  • From the z-score obtained above, the value of the probability p(x < a), can be obtained from the Z-table
  • The value of p(x > a) = 1 - p(x < a)
  • The value of p(a < x < b) is the difference between p(x < a) and p(x > b), the larger first, to get a positive value

4. The normal approximation to the binomial distribution is the use of the

normal (continuous) distribution to approximate the binomial (discrete)

distribution

Using the approximation, we have;

The mean = n·p

The standard deviation, [tex]\sigma = \sqrt{(n \cdot p \cdot (1 - p))}[/tex]

Where;

n = The sample size;

p = The probability value given

With the calculated mean and standard deviation, the z-score and

probability p(x < a), can be found for a particular value, a, using the steps

for solving probability problems involving normal distribution

Learn more here:

https://brainly.com/question/15217335

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