A person invests $1,000 into stock of a company that hopes to go public in one year. The probability that the person will lose all his money after one year (i.e. his stock will be worthless) is 35%. The probability that the person’s stock will still have a value of $1,000 after one year (i.e.no profit and no loss) is 60%. The probability that the person’s stock will increase in value by $10,000 after one year (i.e. will be worth $11,000) is 5%. a) Create a probability model to find the expected profit after one year. b) Find the standard deviation (SD) = √?(?)
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
A person invests $1,000 into stock of a company that hopes to go public in one year. The
person will lose all his money after one year (i.e. his stock will be worthless) is 35%. The probability that the
person’s stock will still have a value of $1,000 after one year (i.e.no profit and no loss) is 60%. The probability
that the person’s stock will increase in value by $10,000 after one year (i.e. will be worth $11,000) is 5%.
a) Create a probability model to find the expected profit after one year.
b) Find the standard deviation (SD) = √?(?)
![### Probability and Expected Value Table
The table below is used to calculate the expected value (E(X)) and variance (V(X)) of different events.
#### Table Structure:
| Event | x | P(x) | x • P(x) | (x – E(X))² • P(x) |
|---------------------------|---|------|----------|-------------------|
| **Lose** | | | | |
| **Profit** | | | | |
| **No profit & no loss** | | | | |
- **Event**: This column lists the possible outcomes, such as "Lose," "Profit," and "No profit & no loss."
- **x**: This column represents the value associated with each event.
- **P(x)**: This column shows the probability of each event occurring.
- **x • P(x)**: This column contains the product of the value x and its probability P(x).
- **(x – E(X))² • P(x)**: This column is used to calculate the variance, showing the product of the squared difference between value x and the expected value E(X), and the probability P(x).
#### Calculations:
- **Expected Value (E(X))**:
\[
E(X) = \sum (x \cdot P(x))
\]
- **Variance (V(X))**:
\[
V(X) = \sum (x - E(X))^2 \cdot P(x)
\]
Use this table and the given formulas to compute the expected value and variance for different scenarios. This is crucial for understanding the distribution and risk associated with different outcomes in probabilistic events.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe25f560c-ab9f-4e77-9262-a728e7296416%2F806c81f6-55ca-4db1-adab-45d451f52c57%2Fzkplm3.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
