Question

We will be comparing empirical probabilities (relative frequencies based on an observation of a real-life process) to theoretical probabilities (long-run relative frequency). We will use StatCrunch to simulate this process of drawing colored balls from an urn without replacement. Imagine this urn has 50 total balls, 18 of which are red and 32 of which are green. You draw 6 balls from the urn and we are interested in the number of red balls that are drawn.

The probability distribution table for the random variable representing the number of red balls drawn from the urn is given in the table below. Using one to two complete sentences, verify that the two features of a discrete probability distribution are valid.

Outcome 0 1 2 3 4 5 6
Probability 0.0570 0.2281 0.3462 0.2547 0.0955 0.0173 0.0012

Answer 1

Answer:

The discrete probability distribution satisfies all the features,

Step-by-step explanation:

We are given the following discrete probability distribution:

Outcome:         0           1                2            3            4            5            6

Probability: 0.0570   0.2281   0.3462   0.2547   0.0955   0.0173   0.0012

Property of discrete probability distribution:

$0<P(x_i)<1$

$\Displaystyle\sum P(x_i) = 1$

Verification:

1. As observed all the probabilities are between 0 and 1.

2.

$\displaystyle\sum P(x_i) =\\\\=0.0570+0.2281+0.3462+0.2547 + 0.0955 +0.0173 +0.0012 = 1$

Thus, the given discrete probability distribution is a valid distribution.