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Exercise 1 A continuous random variable $x$ has a probability density function $$p(\xi) = \begin{cases} \exp(-\xi) & \text{if } \xi \geq 0 \\ 0 & \text{if } \xi < 0. \end{cases}$$ Let $y$ be $\lfloor x \rfloor$, that is, $y$ is the largest integer less than or equal to $x$. Consequently, $y$ is a discrete random variable. (a) Derive the probability mass function of $y$. (10 points) (b) Compute both $\mathbb{E}[x]$ and $\mathbb{E}[y]$. Is $\mathbb{E}[y]$ smaller than $\mathbb{E}[x]$? (15 points)

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Find the slope and y-intercept to graph the equation f(x) = 3x – 5. Slope: y-intercept: Graph the equation. 5 4 3 2 1 -5 -4 -3 -2 -1 1 2 3 4 5 1 -2 -3 -4 -5 Clear All Draw: Submit Question

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Name two ways that wind-pollinated flowers differ from those that utilize pollinators.

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Question Find the derivative of $f(x) = -4 \cos (x) + \sin (x)$ at the point $x = 0$. Do not include "$f'(x) =$" in your answer. For example, if your answer is $f'(x) = 3x + 3$, you wou

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Question #7 • How many nonzero entries does the matrix representing the relation R on A = \{1, 2, 3, ..., 100\} consisting of the first 100 positive integers have if R consists of pairs (a,b), where a is greater than b.

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Marlene spends most of the day thinking about fairies. Sometimes, when she's at school, thoughts about fairies will just pop into her head. Marlene's thoughts about fairies, therefore, sometimes interfere with her school work, but Marlene can't help it--she just loves thinking about fairies. Is Marlene experiencing an obsession with fairies? Group of answer choices Yes. No, because we don't know how long this has been going on. No, because she likes these thoughts. No, because these thoughts don't spur her to complete compulsions.

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Question 5 (1 point) ? Saved After balancing the reaction below, which statement is FALSE regarding it? Cl$_2$(g) + OH$^-$ (aq) ? Cl$^-$ (aq) + ClO$^-$ (aq) + H$_2$O(l) The product ClO$^-$ is a strong disinfectant, known as bleach. This is a disproportionation reaction. The oxidation number of H does not change. One mole of H$_2$O(l) is produced for every mole of OH$^-$ (aq) consumed. One mole of ClO$^-$ (aq) is produced for every mole of Cl$_2$(g) consumed.

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I_x = ? I_c = 12 I_b = -1 I_d = -18 I_y = ? I_g = -7 I_f = 15

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TT biLeg PFlag question A ball of mass m is attached to a rod at point C which has a coefficient of restitution e. Determine the following: 1. The velocity of the ball after the impact. 2. The angular velocity of the rod about the Z axis. 3. The velocity of point C after the impact.

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7. In a barter economy has 10 items, how many price relatives are needed?

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alicia t.