题干

某技术公司新开发了A,B两种新产品,其质量按测试指标划分为:指标大于或等于82为正品,小于82为次品,现随机抽取这两种产品各100件进行检测,检测结果统计如下:

测试指标

[70,76)

[76,82)

[82,88)

[88,94)

[94,100]

产品A

8

12

40

32

8

产品B

7

18

40

29

6

(1)试分别估计产品A,产品B为正品的概率;

(2)生产一件产品A,若是正品可盈利80元,次品则亏损10元;生产一件产品B,若是正品可盈利100元,次品则亏损20元;在(1)的前提下.记X为生产一件产品A和一件产品B所得的总利润,求随机变量X的分布列和数学期望.

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答案(点此获取答案解析)

解:(1)由检测结果统计表,得产品A为正品的概率为:4032100
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    My professor brother and I have an argument about head and heart, about whether he overvalues IQ while I lean more toward EQ. We commonly have this debate about people—can you be friends with a really smart jerk(怪物)?—but that also applies to animals as well .I'd love it if our dog could fetch the morning paper and then read it to me over coffee, but I actually care much more about her loyal and innocent heart. There's already enough thinking going on in our house, and we probably spend too much time in our heads. Where we need some role modeling is in instinct, and that's where a dog is a vivid example.

    I did not grow up with dogs, which meant that my older daughter's respectful but firm determination to get one required some adjustment on my part. I often felt she was training me: from ages of 6 to 9, she gently schooled me in various breeds and their personalities, whispered to the dogs we met with so they would charm and persuade me, demonstrated by her self-discipline that she was ready for the responsibility. And thus came our dog Twist, whom I sometimes mistake for a third daughter.

    At first I thought the challenge would be to train her to sit, to follow, to walk calmly beside us and not go wildly chasing the neighborhood rabbits. But I soon discovered how much more we had to learn from her than she from us.

    If it is true, for example, that the secret to a child's success is less rare genius than raw persistence, Twist's ability to stay on task is a model for us all, especially if the task is trying to capture the sunbeam that touches softly around the living room as the wind blows through the branches outside. She never succeeds, and she never gives up. This includes when she runs straight into walls.

    Then there is her unfailing patience, which breaks down only when she senses that dinnertime was 15 minutes ago and we have somehow failed to notice. Even then she is more eager than annoyed, and her refusal to complain shows a self control of which I'm not always capable when hungry.

    But the lesson I value most is the one in forgiveness, and Twist first offered this when she was still very young. When she was about 7 months old, we took her to the vet to be spayed(切除卵巢). We turned her over to a stranger, who was to perform a procedure that was probably not pleasant. But when the vet returned her to us, weak and tender, there was no accusation, no how could you do that to me? It was as though she already knew that we would not intentionally cause her pain, and while she did not understand, she forgave and curled up with her head on my daughter's lap.

    I suppose we could have concluded that she was just blindly loyal and obedient. But eventually we knew better. She is entirely capable of disobedience, as she has proved many times. She will ignore us when there are more interesting things to look at, scold us when we are careless, bark into the twilight when she has urgent messages to send. But her patience with our failings and carelessness and her willingness to give us a second chance are a daily lesson in gratitude.

    My friends who grow up with dogs tell me how when they were teenagers and trusted no one in the world, they could tell their dog all their secrets. It was the one friend who would not gossip or betray, could provide in the middle of the night the soft, unselfish comfort and peace that adolescence plots to disturb. An age that is all about growth and risk needs some anchors and weights, a stable model when all else is changing. Sometimes I think Twist's devotion keeps my girls on a benevolent leash, one that hangs quietly at their side as they walk fast along but occasionally pulls them back to safety and solid ground.

    We've weighed so many decisions so carefully in raising our daughters---what school to send them to and what church to attend, when to give them cell phones and with what precautions. But when it comes to what really shapes their character and binds our family, I never would have thought we would owe so much to its smallest member.