suppose that the probability density function of the random variable x is given by the graph below. determine the following probabilities. round your answers to 3 digits after the decimal point.
What are the probabilities to be determined from a given probability density function graph?
Answer:
When dealing with a probability density function graph, there are several probabilities that can be calculated based on the graph. Here are some of the common probabilities that can be determined:
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Probability of a Specific Value: The probability of a random variable x taking on a specific value can be determined by finding the point on the graph that corresponds to that value and calculating the area under the curve at that point.
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Probability of a Range of Values (Between Two Values): To find the probability that the random variable x falls between two specific values, you need to calculate the area under the curve between those two values on the graph.
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Cumulative Probability: The cumulative probability of a random variable x being less than or equal to a certain value can be found by calculating the area under the curve up to that value on the graph.
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Conditional Probability: Conditional probability, which is the probability of an event occurring given that another event has already occurred, can also be calculated based on the probability density function graph.
By interpreting the graph correctly and using the properties of probability density functions, you can calculate these probabilities accurately by rounding your answers to 3 digits after the decimal point.