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**enmascarado** Hello guys, we are starting random variables and I know that the mean of a random variable is the function times the probability for all x's (right?), but I am lost with the next two problems. Any help on number 1 would be greatly appreciated, full answer or not. For number 2 I am totally lost.

1. What is the mean of X which has the following density function?

f X (x) = 1/C; for: 0 <= x <= 7

Hint: Find the numerical value of C

2. Consider the probability density function given by:

P X (x) = lambda/2; for: 0<= x <=2

P X (x) = (1 - lambda)/4; for: 2<= x <=6

This is a mixture of two uniform distributions. a)Sketch P X (x) for lambda=0.5. b) Sketch P X (x) for lambda=0.333. c) In a random sample from P X (x), 60% of the values were between 0 and 2. What would be an estimate for the value of lambda?