Density Graphs Worksheet
Grade 12 Math worksheet on understanding and interpreting density graphs in probability and statistics.
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Density Graphs Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work where applicable.
1. Explain, in your own words, what a probability density function (PDF) represents and its key properties.
2. For a continuous random variable X with a probability density function f(x), what does the area under the curve of f(x) between two points 'a' and 'b' represent?
The mean of X
The probability that X is between a and b
The variance of X
The mode of X
3. Consider the following probability density function graph:
Based on the graph, what is the probability that X is between 0 and 2? Assume the maximum height of the function is 1 at x=1.
4. For any valid probability density function f(x), the total area under its curve must always be equal to .
5. A probability density function f(x) can never take on values.
6. For a continuous random variable, P(X = c) = 0 for any specific value c.
True
False
7. A random variable X represents the lifespan of a certain electronic component in years. Its PDF is given by f(x) = 0.5e^(-0.5x) for x ≥ 0 and 0 otherwise. Sketch this PDF and shade the area representing the probability that a component lasts between 1 and 2 years.
Calculate the probability P(1 < X < 2). You may need to use integration.