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Hi there.
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In this question, we are given with a graph and we have four parts to answer.
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That is the first question is we have to explain why the graph serve as a cumulative distribution function.
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And the second one is is x is a discrete random variable.
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Third one is we have to compute the probability of x less than or equal to 2 .4 and probability of 0 less than or equal to x less than 4.
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And in the deep part, if x is discrete, we have to calculate the probability mass function, and if x is continuous, we have to calculate the probability density function of x.
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Let's see how we'll do this.
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In the first part, we have to explain why the function serves as a, or why the graph serves as a cdf.
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So it is because of four main reasons.
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The first one is that f of x, the function value, f of x is equal to zero for all x less than or equal to minus 1.
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And the second thing is f of x is equal to 1 for all x which is greater than or equal to 5.
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That is the function values set to 1 after the values x greater than or equal to 5.
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Now the function values, the function values sum up to 1, sum up to 1 from minus 1 to 5.
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And the fourth point is that f of x is less than or equal to 1 for all x, that is, the function values will go up to 1.
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So because of all these reasons, we can say that the given function graph is a cdf.
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Hence, the given graph serves as a cdf.
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Now we'll move on to the second part.
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In the second part, we have to check whether x is a discrete random variable.
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For that, we'll observe the graph once again.
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So this was the graph.
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From here we'll get the function as fx of x is equal to fx of x is equal to the set 0 if x is less than minus 1.
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So the function value is 0 for all the values less than minus 1.
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Now also we have 0 .2 multiplied by x plus 1 for all the values minus 1 less than or equal to x less than 1.
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So that will be this particular portion, this particular portion.
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The straight line has the equation 0 .2 multiplied by x plus 1.
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Now we'll be having the next one.
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That is 0 .4 if x.
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Varies from 1 and 3 between 1 and 3.
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1 less than or equal to x less than or equal to 3.
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And we'll be having 0 .3 multiplied by x minus 3 plus 0 .4 if x is between 3 and 5, 3 less than or equal to x less than or equal to 5.
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Actually this x less than five now we'll be having one if x is greater than or equal to five so x is if x is greater than equal to five we'll be having uh the value as one so from here we can see that the given function is continuous so the random variable random variable is continuous the given random variable is continuous.
03:46
So we have the given random variable x is not discrete, but it is continuous.
03:56
In the next part, we have to compute probability of x less than equal to 2 .4 and probability of 0 less than or equal to x less than 4.
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For that, we'll observe the graph and this function.
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So first we'll be having probability, we'll be finding probability of x less than or equal to 2 .4.
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From this function it is clear that probability of x less than or equal to 2 .4 is 0 .4...